ORIGINAL_ARTICLE
λ- semi compact spaces and λ- strongly compact spaces
For an infinite cardinal number λ , λ- semi compact spaces and λ-strongly compact spaces which are generalizations of semi-compact spaces and strongly compact spaces are introduced and studied. It is shown that for every infinite cardinal number λ , there exist non-discrete λ- semi compact spaces and non-discrete λ- strongly compact spaces. Basic properties of such spaces are investigated.
https://jamm.scu.ac.ir/article_16421_beca314973ae1af9376f9e703e050bd9.pdf
2021-04-21
1
10
10.22055/jamm.2021.34921.1852
λ- semi compact
λ- strongly compact
λ-semi normal
Masoumeh
Etebar
m.etebar@scu.ac.ir
1
Department of Mathematics, Faculty of Mathematics and Mathematical Sciences, Shahid Chamran University of Ahvaz, ,Ahvaz, Iran
AUTHOR
Mohammad Ali
Siavoshi
m.siavoshi@scu.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences and computer, Shahid Chamran University of Ahvaz,, Ahvaz, Iran
LEAD_AUTHOR
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27
ORIGINAL_ARTICLE
Stability of a System of Euler-Lagrange Type Cubic Functional Equations in non-Archimedean 2-Normed Spaces
Freese and Cho have introduced the non-Archimedean 2-normed spaces and Eshaghi, et al. have introduced the Menger probabilistic non-Archimedean 2-normed spaces. In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of Euler-Lagrange type cubic functional equations in the non-Archimedean 2-normed spaces. Also, we prove the generalized Hyers-Ulam-Rassias stability for this system in the Menger probabilistic non–Archimedean 2–normed spaces.
https://jamm.scu.ac.ir/article_16422_ef19d3a627fc492830b7f923db25bd0a.pdf
2021-04-21
11
24
10.22055/jamm.2020.28513.1685
Euler-Lagrange type cubic functional equations
Non-Archimedean 2-Normed spaces
Menger Probabilistic Non-Archimedean 2–Normed spaces
Generalized Hyers-Ulam-Rassias stability
Hamid
Majani
majani.hamid@gmail.com
1
Department of mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran.
LEAD_AUTHOR
[1] S. Gähler, 2-metrische Räume und ihre topologische Struktur, Math. Nachr. 26 (1963) 115-148.
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[2] S. Gähler, Lineare 2-normierte Räumen, Math. Nachr. 28 (1964) 1-43.
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[4] A. White, 2-Banach spaces, Doctorial Diss., St. Louis Univ., 1968.
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[7] Z. Lewandowska, Generalized 2-normed spaces, Slupskie Prace Matematyczno- Fizyczne 1, 33-40(2001).
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[8] Z. Lewandowska, On 2-normed sets, Glas. Mat. Ser. III 38 (1) 99-110 (2003).
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[9] Z. Lewandowska, Banach-Steinhaus theorems for bounded linear operators with values in a generalized 2-normed space, Glas. Mat. Ser. III 38 (2) 329-340 (2003).
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[10] Z. Lewandowska, Bounded 2-linear operators on 2–normed sets, Glas. Mat. Ser. III 39 (2) 301-312 (2004).
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[11] W. -G. Park, Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011) 193-202.
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[12] K. Hensel, Über eine neue Begründung der Theorie der algebraischen Zahlen, Jahresber. Deutsch. Math. Verein 6 (1897) 83-88.
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[13] V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-adic Analysis and Mathematical Physics, World Scientific, 1994.
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[14] A. Khernikov, non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.
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[15] R. W. Freese, Y. Cho, Geometry of Linear 2-Normed Spaces, Nova Science Publishers, 2001.
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[16] A. N. Srstnev, On the motion of a random normed space, Dokl. Akad. Nauk SSSR 149 (1963), 280-283 English translation in Soviet Math. Dokl. 4 (1963) 388-390.
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[19] M. Eshaghi Gordji, M. B. Ghaemi, Y. J. Cho and H. Majani, A General System of Euler–Lagrange-Type Quadratic Functional Equations in Menger Probabilistic Non-Archimedean 2-Normed Spaces, Abs. Appl. Anal., Volume 2011, Article ID 208163, 21 pages.
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[25] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300.
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[26] P. Găvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994) 431-436.
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[27] L. M. Arriola and W. A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Anal. Exchange 31 (2005/2006), 125-132.
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[28] M. Eshaghi Gordji, M. B. Ghaemi and H. Majani, Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces, Discrete Dyn. Nat. Soc., Volume 2010, Article ID 162371, 11 pages.
28
[29] M. Eshaghi Gordji, M. B. Ghaemi, H. Majani and C. Park, Generalized Ulam–Hyers Stability of Jensen Functional Equation in Serstnev PN Spaces, J. Ineq. Appl., Volume 2010, Article ID 868193, 14 pages.
29
[30] M. Eshaghi and H. Khodaei, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear Anal. 71 (2009) 5629-5643.
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[31] H. Khodaei, On the stability of additive, quadratic, cubic and quartic set-valued functional equations, Results Math. 68 (2015) 1-10.
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[32] K. -W. Jun and H. -M. Kim, On the stability of Euler-Lagrange type cubic mappings in quasi-Banach spaces, J. Math. Anal. Appl. 332 (2007) 1335-1350.
32
ORIGINAL_ARTICLE
Stability and Permanency in a mathematical model for reciprocal effect of water resources and population
In this paper, we will introduce a mathematical model, based on prey-predator models, to study reciprocal effects of water resources and population. First, we will construct the model and introduce the parameters and variables of the system. Next we will study local behaviors around inner equilibrium points and global behaviors in the admissible region of the system. Especially we will see that how changes of the parameters might cause simultaneous permanency/impermanency of population and water resources through local bifurcations and changes in the structure of solutions
https://jamm.scu.ac.ir/article_16423_82cfc18082f2f6e058b5ecbd2d7b6243.pdf
2021-04-21
25
39
10.22055/jamm.2020.30924.1754
Permanency
Prey-Predator systems
local bifurcations
Water resources
omid
rabieimotlagh
orabieimotlagh@birjand.ac.ir
1
associate professor/Faculty of Mathematics and Statistics University of Birjand
LEAD_AUTHOR
Hajimohammad
Mohammadinejad
hmohammadin@birjand.ac.ir
2
University of Birjand, Birjand, Iran
AUTHOR
[1] P.H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika, 35 (1948) 213–245.
1
[2] R.K. Upadhyay and S.R.K. Iyengar, Introduction to mathematical modeling and chaotic dynamics, CRC Press, First Edition. A Chapman and Hall Book, 2014.
2
[3] Y. Cia, C. Zhao, and W. Wang, Dynamics of a leslie-gower predator-prey model with additive allee effect, Applied Mathematical Models, 39 (2015) 2092–2106.
3
[4] J.B. Collings, The effect of the functional response on the bifurcation behavior of a mite predator-prey interaction model, Journal of Mathematical Biology, 36 (1997) 149–168.
4
[5] P.M. Dolman, The intensity of interference varies with resource density: evidence from a field study with snow buntings, plectrophenax nivalis, Oecologia, 102 (1995) 511–514.
5
[6] C. Jost and R. Arditi, From pattern to process: identifying predator-prey interactions, Population Ecosystems, 43 (2001) 229–243.
6
[7] R. KhoshsiarGhazian, J. Alidoust and A. BayatiEshkaftakib, Stability and dynamics of a fractional order leslie-gower prey-predator model, Applied Mathematical Modelling, 40 (2016) 2075–2086.
7
[8] R.E. Koiji and A. Zegeling, Qualitative properties of two-dimensional predator- prey system, Journal of Nonlinear Analysis, 29 (1997) 693–715.
8
[9] Y. Kuang and H.I. Freedman, Uniqueness of limit cycles in gause type models of predator-prey systems, mathematical Bioscience, 88 (1988) 67–84.
9
[10] R. Arditi and L.R. Ginzburg, Coupling in predator-prey dynamics: ratio dependence, Journal of Theoretical Biology, 139 (1989) 311–326.
10
[11] H. Baek, A food chin system with holling type iv functional response and impulsive perturbations, Computers and Mathematics with Applications, 60 (2010) 1152–1163.
11
[12] J. Huang, S. Ruan, and J. Song, Bifurcations in a predator-prey system of leslie type with generalized holling type iii functional response, Journal of Differential Equations, 257 (2014) 1721–1752.
12
[13] SH. Li, J. Wu, and H. Nie, Positive steady state solutions of a leslie-gower predator-prey model with holling type ii functional response and density dependent diffusion, Journal of Nonlinear Analysis, 82 (2013) 47–65.
13
[14] Y. Li and D. Xiao, Bifurcations of a predator prey system of holling and leslie types, Chaos, Solitons and Fractals, 34 (2007) 606–620.
14
[15] Z. Liang and H. Pan, Qualitative analysis of a ratio-dependent holling- tanner model, Journal of Mathematical Analysis and Application, 334 (2007) 954–962.
15
[16] H. Qulizadeh, O. RabieiMotlagh, and H.M. Mohammadinejad, Permanency in predator–prey models of leslie type with ratio-dependent simplified holling type-iv functional response, Mathematics and Computers in Simulation, 157 (20198) 63–76.
16
[17] S. Ruan and D. Xiao, Global analysis in a predator-prey system with nonmonotonic functional response, SIAM Journal of Applied Mathematics, 61 (2001) 1445–1472.
17
[18] G.T. Skalski and J.F. Gilliam, Functional responses with predator interference: viable alternatives to the holling type ii model, Ecology, 82 (2001) 3083–3092.
18
[19] Y. Tzung-shin, Classiffication of bifurcation diagram for a multiparameter diffusive logistic problem with holling type iv functional response, Journal of Mathematical Analysis and Application, 418 (2014) 283–304.
19
[20] L. Perko, Differential Equations and Dynamical Systems, Springer, First Edition. New York, (1996).
20
[21] P. Milman, The malgrange-mather division theorem, Topology, 16 (1977) 395–401.
21
ORIGINAL_ARTICLE
Locally constant functions and oc-paracompact spaces
In this article we investigate and study the ring LC(X) of all real-valued locally constant functions on a topological space X . We show that X is a connected space if and only if LC(X)=R. If X is a compeletly regular and Hausdorff space, we show that LC(X) is always Von Neumann regular ring and also we prove that LC(X)=∩{xin N}(R+Ox) which N is the set of all non-isolated points of X . Also we show that X is a P-space if and only if LC(X)=C(X), where C(X) denotes the ring of all real-valued continuous functions . It is also shown that X is a weakly pseudocompact space if and only if LC(X)=CF(X) , where CF(X) denotes the ring of all real-valued continuous functions with finite image. In case X is Lindel of, we prove that it is a CP-space if and only if LC(X)=CC(X), where CC(X) denotes the ring of all real-valued continuous functions with countable image. We introduce the concept of "oc-paracompact" and we observe that an oc-paracompact space is compact if and only if it is weakly pseudocompact. Finally, we show that if X is a zero dimensional and second countable space , then X is compact if and only if it is a weakly pseudocompact space.
https://jamm.scu.ac.ir/article_16424_a2b3a5a6cd24a0a3b553974a64d8aace.pdf
2021-04-21
40
48
10.22055/jamm.2020.32050.1788
Locally constant function
P-space
oc-paracompact space
weakly pseudcompact space
Rostam
Mohamadian
mohamadian_r@scu.ac.ir
1
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
LEAD_AUTHOR
[1] F. Azarpanah and O.A.S. Karamzadeh and Z. Keshtkar and A.R. Olfati, On maximal ideals of C_c(X) and the uniformity of its localizations, Rocky Mt. J. Math., 48 (2018) 345–384.
1
[2] F. Azarpanah and M. Namdari and A.R. Olfati, On Subrings of the form I + R of C(X), Journal of Commutative Algebra, 11(4) (2019) 479–509.
2
[3] R. Engelking, General Topology, Sigma Ser. Pure Math,Vol. 6, Heldermann, Berlin, 1989.
3
[4] M. Ghadermazi and O.A.S. Karamzadeh and M. Namdari, On the functionally countable subalgebra of C(X) , Rend. Sem. Mat. Univ. Padova, 129 (2013) 47–69.
4
[5] M. Ghadermazi and O.A.S. Karamzadeh and M. Namdari, C(X) versus its functionally countable subalgebra, Bull. Iranian Math. Soc., 45 (2019) 173–187.
5
[6] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York,1976.
6
[7] J. Hart and K. Kunen, Locally constant functions, Fund. Math., 1976.150 (1996), 67– 96.
7
[8] O.A.S. Karamzadeh and M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X) , Appl. Gen. Topol. 16 (2) (2015) 183–207 .
8
[9] M. Namdari and A. Veisi, The subalgebra of Cc(X) consisting of elements with countable image versus C(X) with respect to their rings of quotients, Far East J. Math. Sci. (FJMS), 59 (2011) 201–212 .
9
[10] M.E Rudin and W. Rudin, Continuous Functions That Are Locally Constant on Dense Sets, J. Funct. Anal., 133 (1995), 129 137.
10
[11] S. Wilard, General Topology, Addison-Wesley Publishing Company, Inc., Reading Mass., 1970.
11
ORIGINAL_ARTICLE
Dynamic analysis of the fractional predator-prey system based on the Mittag-Leffler function
In this paper, the dynamic behavior of a fractional-order predator-prey system based on the Mittag-Leffler function is investigated. First, we study the existence, uniqueness, non-negativity, and boundedness for the solution of this fractional-order system. Then, we show that this system has two different equilibrium points. Some sufficient conditions to ensure the global asymmetric stability of these points are also proposed by using the Lyapunov function. Finally, we present some numerical simulations to confirm the analytical results.
https://jamm.scu.ac.ir/article_16668_c0ccddc1a33e8f36a9fd18695aaff0ce.pdf
2021-04-21
49
60
10.22055/jamm.2020.33065.1808
Fractional-order Predator-prey system
Caputo derivative
Mitag-Leffler function
asymptotic stability
Shahnaz
Mohamadi
sh_mohammadi@sut.ac.ir
1
Department of Mathematics, Sahand University of Technology, Tabriz, Iran
AUTHOR
Fridoun
Moradlou
fridoun.moradlou@gmail.com
2
Department of Mathematics, Sahand University of Technology, Tabriz, Iran
LEAD_AUTHOR
Mojtaba
Hajipour
hajipour@sut.ac.ir
3
Department of Mathematics, Sahand University of Technology, Tabriz, Iran
AUTHOR
[1] I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, in: fractional differential equations, to methods of their solution and some of their applications, Academic Press, New York, 1999 .
1
[2] J. Sabatier, M. Aoun, A. Oustaloup, G. Gregoire, F. Ragot, P. Roy, Fractional system identification for lead acid battery state of charge estimation, Signal processing 86 (2006) 2645–2657.
2
[3] J. D. Gabano, T. Poinot, Fractional modelling and identification of thermal systems, Signal Processing 91 (2011) 531–541.
3
[4] D. Baleanu, Fractional calculus: models and numerical methods, World Scientific, 2012.
4
[5] A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Thermal Science 20 (2016) 763–769.
5
[6] D. Baleanu , A. Fernandez, On some new properties of fractional derivatives with Mittag-Leffler kernel, Communications in Nonlinear Science and Numerical Simulation 59 (2018) 444–462.
6
[7] D. Baleanu, A. Jajarmi, M. Hajipour, On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel, Nonlinear Dynamics 94 (2018) 397–414.
7
[8] V. Volterra, Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Mem. Acad. Lincei Roma. 2 (1926) 31–113.
8
[9] J. D. Murray, Mathematical Biology, Spring-Verlag, New York, Berlin, 1993.
9
[10] J. P. Tripathi , S. Abbas, M. Thakur, Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge, Nonlinear Dynamics 80 (2015) 177–96.
10
[11] Y. Huang , F. Chen, L. Zhong, Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge, Applied Mathematics and Computation 182 (2006) 672–83.
11
[12] E. Ahmed, A. M. El-Sayed H. A. El-Saka. Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models, Journal of Mathematical Analysis and Applications 325 (2007) 542–553.
12
[13] H. L. Li, L. Zhang, C. Hu, Y. L. Jiang Z. Teng, Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge, Journal of Applied Mathematics and Computing 54 (2016) 435–49.
13
[14] A. A. Elsadany, A. E. Matouk, Dynamical behaviors of fractional-order Lotka-Volterra predator-prey model and its discretization, Journal of Applied Mathematics and Computing 49 (2015) 269–83.
14
[15] F. A. Rihan, S. Lakshmanan A. H Hashish, Rakkiyappan R. Ahmed E., Fractional-order delayed predator-prey systems with Holling type-II functional response, Nonlinear Dynamics 80 (2015) 777–89.
15
[16] B. K. Lenka, S. Banerjee, Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems, Communications in Nonlinear Science and Numerical Simulation 56 (2018) 365–79.
16
ORIGINAL_ARTICLE
A criterion for selecting a two level fractional factorial design
Application of fractional factorial design is common in experiments with a large number of factors. Choosing the appropriate fraction is an important issue in the fractional designs literature. There are different criteria based on different perspectives. In this paper, a criterion based on minimization of a weighted function of the mean squared error matrix of the least squares estimators of a pre-specified model is introduced. In two-level fractional designs, the criterion for the uniform weight function is calculated and shown to be equivalent to the well-known $ D $-optimal design. Finally, the method is described with examples.
https://jamm.scu.ac.ir/article_16745_6698e991c76432ff2d69f1d50dc23fcd.pdf
2021-04-21
61
68
10.22055/jamm.2021.29978.1731
Fractional factorial design
optimal design
Two level design
Nabaz
Esmailzadeh
n.esmailzadeh@uok.ac.ir
1
Department of Statistics, University of Kurdistan, Sanandaj, Iran
LEAD_AUTHOR
Shayda
Ramezani
shaydaramezani67@gmail.com
2
Department of Statistics, University of Kurdistan, Sanandaj, Iran
AUTHOR
[1] Box G. E. P. and Hunter J. S., The 2^k fractional factorial designs: part I, Technometrics, 3 (1961a),311-351.
1
[2] Box G. E. P. and Hunter J. S., The 2^k fractional factorial designs: part II, Technometrics, 3 (1961b), 449-458.
2
[3] Cheng C. S., Orthogonal arrays with variable numbers of symbols, Ann. Stat., 8 (1980), 447-453.
3
[4] Fedorov V. V., Theory of optimal experiments, Academic Press, New York, (1972).
4
[5] Lehmann E. L. and Romano J., Testing Statistical Hypotheses, Springer, New York, (2005).
5
[6] Lin D. K. J. and Zhou J., D-optimal minimax fractional factorial designs, Can. J. Stat., 41 (2013), 325-340.
6
[7] Pukelsheim F., Optimal design of experiments, Wiley, New York, (1993).
7
[8] Rao C. R., Linear Statistical Inference and its Applications, Wiley, New York, (1973).
8
[9] Tang B. and Zhou J., Existence and construction of two-level orthogonal arrays for estimating main effects and some specified two-factor interactions, Stat. Sin., 19 (2009), 1193-1201.
9
[10] Wilmut M. and Zhou J., D-optimal minimax design criterion for two-level fractional factorial designs, J. Stat. Plan. Inference., 141 (2011), 576-587.
10
[11] Wu C. F. J. and . Hamada M. S, Experiments: planning, analysis and optimization, Wiley, New York,(2009).
11
[12] Yin Y. and Zhou J., Minimax design criterion for fractional factorial designs, Ann. Inst. Stat. Math. 67 (2015), 673-685.
12
ORIGINAL_ARTICLE
Global dynamics of a mathematical model for propagation of infection diseases with saturated incidence rate
An epidemic model is described and introduced in which a vaccination program has been included. The model considers disease-caused death in addition to natural death, and the total population size is variable. The equilibria of the model, the disease-free equilibrium and the endemic equilibrium, are obtained and the global dynamics of the model are stated via the basic reproduction number using proper Lyapunov functions. The disease-free equilibrium is asymptotically globally stable when this quantity is less than or equal to unity and when it is greater than unity, the endemic equilibrium is asymptotically globally stable.
https://jamm.scu.ac.ir/article_16746_102407dfff146ada8e9eec6018079706.pdf
2021-04-21
69
81
10.22055/jamm.2020.33801.1822
epidemic model
immunity
vaccination
global stability
Lyapunov function
Mahmood
Parsamanesh
mahmood.parsamanesh@gmail.com
1
Department of Mathematics, Faculty of Mohajer, Isfahan Branch, Technical and Vocational University, Isfahan, Iran
LEAD_AUTHOR
Majid
Erfanian
erfaniyan@uoz.ac.ir
2
Department of Mathematics, Faculty of Science, University of Zabol,, Zabol, Iran
AUTHOR
[1] Brauer F. and Castillo-Chavez C., Mathematical models in population biology and epidemiology, Springer, 2012.
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[25] Parsamanesh M. and Farnoosh R., On the global stability of the endemic state in an epidemic model with vaccination, Mathematical Sciences, 12(4) (2018), 313–320.
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[26] Parsamanesh M. and Mehrshad S., Stability of the equilibria in a discrete-time SIVS epidemic model with standard incidence, Filomat, 33(8) (2019), 2393–2408.
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[27] Safan M. and Rihan F.A., Mathematical analysis of an SIS model with imperfect vaccination and backward bifurcation, Mathematics and Computers in Simulation, 96 (2014), 195–206.
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32
ORIGINAL_ARTICLE
EXISTENCE AND UNIQUENESS RESULTS FOR IMPULSIVE
FRACTIONAL BOUNDARY VALUE PROBLEM IN BANACH
SPACES
This paper presents several sufficient conditions for the existence of at least one weak solution for the impulsive nonlinear fractional boundary value problem. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.
https://jamm.scu.ac.ir/article_16749_9cfc4b62179e2042471d4c17bd9f1886.pdf
2021-04-21
82
96
10.22055/jamm.2021.34612.1843
Fractional differential equations
One weak solution
Impulsive effect
Variational methods
Ghasem
Alizadeh Afrouzi
afrouzi@umz.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
LEAD_AUTHOR
Shahin
Moradi
sh.moradi@umz.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
AUTHOR
[1] Afrouzi, G.A., Hadjian, A. and Molica Bisci, G. (2013), Some remarks for one-dimensional mean curvature problems through a local minimization principle, Adv. Nonlinear Anal. 2, 427-441.
1
[2] Bai, C. (2011), Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl. 384, 211-231.
2
[3] Bai, C. (2011), Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89, 1-19.
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[4] Benson, D., Wheatcraft, S. and Meerschaert, M. (2000), Application of a fractional advection dispersion equation, Water Resour. Res. 36, 1403-1412.
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[5] Benson, D., Wheatcraft, S. and Meerschaert, M. (2000), The fractional-order governing equation of Lévy motion, Water Resour. Res. 36, 1413-1423.
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[6] Bonanno, G. and Molica Bisci, G. (2009), Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl. 2009, 1-20.
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[7] Bonanno, G., Rodríguez-López, R. and Tersian, S. (2014), Existence of solutions to boundary-value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 3, 717-744.
7
[8] Chen, J. and Tang, X.H. (2012), Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory, Abstr. Appl. Anal. 2012, 1-12.
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[9] Diethelm, K. (2010), The Analysis of Fractional Differential Equation, Springer, Heidelberg.
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[10] Drábek, P. and Milota, J. (2007), Methods of Nonlinear Analisis; Applications to Differential equations, Birkhäuser Verlag AG, Basel, Boston, Berlin.
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[12] Fec̆kan, M., Wang, M. and Zhou, Y. (2011), On the new concept of solutions and existence results for impulsive fractional evolution equations, Dyn. Partial Differ. Equ. 8, 345-361.
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[13] Galewski, G. and Molica Bisci, G. (2016), Existence results for one-dimensional fractional equations, Math. Meth. Appl. Sci. 39, 1480-1492.
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[14] Gao, Z., Yang, L. and Liu, G. (2013), Existence and uniqueness of solutions to impulsive fractional integro-differential equations with nonlocal conditions, Appl. Math. 4, 859-863.
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[15] Guo, L. and Zhang, X. (2014), Existence of positive solutions for the singular fractional differential equations, J. Appl. Math. Comput. 44, 215-228.
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[16] Heidarkhani, S. (2014), Multiple solutions for a nonlinear perturbed fractional boundary value problem, Dynamic. Sys. Appl. 23, 317-331.
16
[17] Heidarkhani, S., Afrouzi, G.A., Ferrara, M., Caristi, G. and Moradi, S. (2018), Existence results for impulsive damped vibration systems, Bull. Malays. Math. Sci. Soc. 41, 1409-1428.
17
[18] Heidarkhani, S., Afrouzi, G.A., Moradi, S., Caristi, G. and Ge, B. (2016), Existence of one weak solution for p(x)-biharmonic equations with Navier boundary conditions, Zeitschrift fuer Angewandte Mathematik und Physik, 67, 73.
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[19] Heidarkhani, S., Ferrara, M. and Salari, A. (2015), Infinitely many periodic solutions for a class of perturbed second-order differential equations with impulses, Acta. Appl. Math. 139, 81-94.
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[20] Heidarkhani, S. and Salari, A. (2020), Nontrivial solutions for impulsive fractional differential systems through variational methods, Math. Meth. Appl. Sci. 43, 6529-6541.
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[21] Heidarkhani, S., Zhao, Y., Caristi, G., Afrouzi, G.A. and Moradi, S. (2017), Infinitely many solutions for perturbed impulsive fractional differential systems, Appl. Anal. 96, 1401-1424.
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[22] Hilfer, R. (2020), Applications of Fractional Calculus in Physics, World Scientific, Singapore.
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[23] Jiao, F. and Zhou, Y. (2011), Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62, 1181-1199.
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[24] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006), Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
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[25] Kong, L. (2013), Existence of solutions to boundary value problems arising from the fractional advection dispersion equation, Electron. J. Diff. Equ., Vol. 2013, No. 106, pp. 1–15.
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[26] Lakshmikantham, V., Baĭnov, D.D. and Simeonov, P.S. (1989), Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA.
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[29] Risken, H. (1998), The Fokker-Planck Equation, Springer, Berlin.
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33
ORIGINAL_ARTICLE
Investigation the boundary and initial value problems including fractional
integro-differential equations with singular kernels
In this paper, the initial and boundary value problems which includes singular fractional integro-differential equations, are investigated. The fractional derivative which is considered in this article, is the Caputo fractional derivative. The integral equations which are discussed in this paper either without any singularity or contain singular kernels that can be weak or strong. In addition to, in this paper to check and study the singularity and regularity of this type of integral equations are paid. Also, the given integral equations are in the form of initial and boundary value problems, which are discussed in terms of the number and manner of boundary conditions. Finally, some examples are provided for the accuracy and efficiency of the method.
https://jamm.scu.ac.ir/article_16754_c6167c953d970a9477df00345a912ce1.pdf
2021-04-21
97
108
10.22055/jamm.2021.34670.1848
fractional integro-differential equation
singular
weak singularity
Mohammadhossein
Derakhshan
m.h.derakhshan.20@gmail.com
1
Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
LEAD_AUTHOR
Mohammad
Jahanshahi
jahanshahi@azaruniv.edu
2
Faculty of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
hamdam
kazemi demneh
kazemi.hamdam@azaruniv.ac.ir
3
Faculty of Mathematics, Azarbaijan Shahid Madani University Tabriz, Iran
AUTHOR
[1] Jahanshahi, M., Ahmadkhanlu, A. (2014). On Well-Posed of Boundary Value Problems Including Fractional Order Differential Equation, Asian. Bull. Math., 36, 53-59.
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[2] Chu, J., O’Regan, D. (2010). Singular integral equation and applications to conjugate problems, Taiwan. J. Math., 14, 329-345.
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[3] Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type: Springer Science & Business Media, 2010.
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[6] Kilbas, A. A., Saigo, M., Saxena, R. K. (2004). Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral. Transform. Spec. Funct., 15, 31-49.
6
[7] Jahanshahi, S., Babolian, E., Torres, D. F., Vahidi, A. (2015). Solving Abel equations of kind first kind via fractional calculus, J. King. Saud. Univ. Sci., 27, 161-167.
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[8] kondo, J. (1991). Integral Equations, Kodansha Tokyo, Clarendon Press Oxford.
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[9] Keshavarz, E., Ordokhani, Y. (2019). A fast numerical algorithm based on the Taylor wavelets for solving the fractional integro-differential equations with weakly singular kernels, Math. Methods. Appl. Sci., 42, 4427-4443.
9
[10] Kanwal, R. P. (2013). Linear integral equations, Springer Science & Business Media.
10
[11] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, 204, Elsevier (North-Holland) Science Publishers, Amsterdam.
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[12] Leonard, A., Mullikin, T. W. (1964). An application of singular integral equation theory to a linearized problem in couette flow, Ann. Phys., 30, 235-248.
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[13] Makroglou, A. (2003). Integral equations and actuarial risk management: Some models and numerics, Math. Modell. Anal. 8, 143-54.
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[14] Nemati, S., Lima, P. (2018). Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions, Appl. Math. Comput., 327, 79-92.
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[15] Nemati, S., Sedaghat, S., Mohammadi, I. (2016). A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels, J. Comput. Appl. Math., 308, 231-242.
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[16] Susahab, D. N., Shahmorad, S., Jahanshahi, M. (2015). Efficient quadrature rules for solving nonlinear fractional integro-differential equations of the Hammerstein type, Appl. Math. Model. 39, 5452-5458.
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[17] Peskin, E. N., Daniel, V.(1995). Schroeder, An Introduction to Quantum Field Theory, Perseus Books Publishing, L.L.C.
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[18] Sabermahani, S., Ordokhani, Y. (2020). A new operational matrix of Müntz-Legendre polynomials and Petrov Galerkin method for solving fractional Volterra-Fredholm integrodifferential equations, Comput. Methods. . Differ. Equ. 8, 408-423.
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[19] Sabermahani, S., Ordokhani, Y., Yousefi, S. A. (2018). Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations, Comput. Appl. Math. 37, 3846-3868.
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22
ORIGINAL_ARTICLE
Natural convection porous fin with temperature-dependent thermal conductivity
and internal heat generation via optimized Chebyshev polynomials with interior
point algorithm
In this study, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature dependent thermal conductivity is revisited. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of different parameters on the thermal performance of the porous fin. Regarding the problem formulation, a novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing nonlinear differential equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Furthermore, the obtained results are more accurate than those reported in previous researches.
https://jamm.scu.ac.ir/article_16750_ee46254ec25b9325fcd244fd40cdc756.pdf
2021-04-21
109
123
10.22055/jamm.2021.35045.1855
Chebyshev polynomial of the first kind
Interior point method
Natural convection
Porous Fin
Thermal performance
Temperature-dependent thermal conductivity
Internal heat generation
Elyas
Shivanian
shivanian@sci.ikiu.ac.ir
1
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran
LEAD_AUTHOR
Mahdi
Keshtkar
keshtkarmahdi@gmail.com
2
Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
AUTHOR
Hedayat
Fatahi
fatahi_iau@yahoo.com
3
Department of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.
AUTHOR
[1] S. Abbasbandy, E. Magyari, and E. Shivanian, The homotopy analysis method for multiple solutions of nonlinear boundary value problems, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009) 3530–3536.
1
[2] S. Abbasbandy and E. Shivanian, Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Commun. Nonlinear Sci. Numer. Simulat., 15 (2010) 3830–3846.
2
[3] S. Abbasbandy and E. Shivanian, Predictor homotopy analysis method and its application to some nonlinear problems, Commun. Nonlinear Sci. Nmer. Simulat., 16 (2011) 2456–2468.
3
[4] A. Akgül and M.S.Hashemi, Group preserving scheme and reproducing kernel method for the Poisson–Boltzmann equation for semiconductor devices, Nonlinear Dynamics 88(4) (2017) 2817-2829.
4
[5] M. Anbarloei and E. Shivanian, Exact closed-form solution of the nonlinear fin problem with temperaturedependent thermal conductivity and heat transfer coefficient, Journal of Heat Transfer, 138(11) (2016) 114501.
5
[6] N.H. Asmar, Partial differential equations with Fourier series and boundary value problems, Courier Dover Publications, (2016).
6
[7] D. Bhanja and B. Kundu, Thermal analysis of a constructal t-shaped porous fin with radiation effects. international journal of refrigeration, 34(6) (2011) 1483–1496.
7
[8] M.T. Darvishi, R. Subba, R. Gorla, F. Khani, and A. Aziz, Thermal performance of a porus radial fin with natural convection and radiative heat losses, Thermal Science, 19(2) (2015) 669–678.
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[9] N. Duvvuru and K.S. Swarup, A hybrid interior point assisted differential evolution algorithm for economic dispatch, IEEE Transactions on Power Systems, 26(2) (2011) 541–549.
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[10] D.D. Ganji, The application of he’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A, 335 (2006) 337–341.
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[12] R. Gorla, R.S. Darvishi, and M.T. Khani, Effects of variable thermal conductivity on natural convection and radiation in porous fins, Int. Commun. Heat Mass Transfer, 38 (2013) 638–645.
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[13] M.S. Hashemi, A novel simple algorithm for solving the magneto-hemodynamic flow in a semiporous channel, European Journal of Mechanics-B/Fluids 65 (2017) 359-367.
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[15] M. Hatami and D.D. Ganji, Thermal performance of circular convective–radiative porous fins with different section shapes and materials, Energy Conversion and Management, 76 (2013) 185–193.
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46
ORIGINAL_ARTICLE
Supply Chain Network Design Under Uncertainty: A Case Study Research in Fast Moving Consumer Goods
In this paper, a bi-objective closed-loop supply chain has been studied by Robust Possibilistic Programming (RPP) approach. This paper aims to minimize the cost and product shipping time (delivery) to the customers. The KVSS and MK company are considered a case study of Iran’s vegetable oil industry. This paper addresses -and models- some challenges of this industry and provides the RPP solution approach with appropriate solutions. The main challenge of this industry is that the supply of raw materials and oilseeds is highly dependent on other countries. Accordingly, many other factors such as the exchange rate, sanctions, governmental rules and regulations, custom tariffs, and the supply and demand process, etc., have an impact on the definitive decision-making. Hence, the data are considered uncertain and the RPP approach is used to solve the model. The solving approach is also used to decide on the bi-objective function, in which managers can easily decide on the complex processes of this industry. Finally, the results of the model and the sensitivity analysis are presented to validate the model. The validation process uses examples and practical analyses that have been localized based on Iran’s conditions.
https://jamm.scu.ac.ir/article_16715_872dc675cebe5995a513d0a3842d3a75.pdf
2021-04-21
124
168
10.22055/jamm.2020.30168.1738
Fast moving consumer goods
Robust Possibilistic programming
Closed loop supply chain network design
bi-objective optimization
Hamed
Pouralikhani
hamed_pouralikhani@aut.ac.ir
1
Deparment of Industrial Engineering, Kharazmi University
LEAD_AUTHOR
bahman
Naderi
bahman.naderi@aut.ac.ir
2
Deparment of Industrial Engineering, Kharazmi University
AUTHOR
Alireza
Arshadi khamseh
alireza.arshadikhamseh@gmail.com
3
Deparment of Industrial Engineering, Kharazmi University
AUTHOR
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4. ایران پناه، نصراله، نوری امامزاده، سمانه، «آزمونهای کلاسیک و بوت استرپ برابری میانگینها»، نشریه علوم دانشگاه خوارزمی، سال چهاردهم، شماره دوم، 1393، ص ص: 96-83.
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9. سجاد، رسول، گرجی، مهسا، «برآورد ارزش در معرض خطر با استفاده از روش بازنمونهگیری بوت استرپ (مطالعه موردی بورس اوراق بهادار تهران)»، فصلنامه علمی- پژوهشی مطالعات اقتصادی کاربردی در ایران، دوره اول، شماره یکم، 1391، ص ص: 164-137.
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10. راسخی، سعید؛ خانعلی پور، امیر؛ خسروانی، فاطمه (1393). ﺍﺭﺯﻳﺎﺑﻲﺧﺎﻧﻮﺍﺩﻩ مدلهای GARCH ﺩﺭ پیشبینی ﻧﻮﺳﺎﻧﺎﺕ ﺑﺎﺯﺍﺭ ( ﻣﻄﺎﻟﻌﻪ ﻣﻮﺭﺩﻱ: ﺑﺎﺯﺍﺭ ﺑﻮﺭﺱ ﺍﻭﺭﺍﻕ ﺑﻬﺎﺩﺍﺭ ﺗﻬﺮﺍﻥ ). ﻛﻨﻔﺮاﻧﺲ بینالمللیﺣﺴﺎﺑﺪاری، اﻗﺘﺼﺎد و ﻣﺪﻳﺮﻳﺖﻣﺎﻟﻲ، تهران.
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11. راعی، رضا؛ فلاح طلب، حسین (1392). ﮐﺎرﺑﺮد شبیهسازی مونتکارلو و ﻓﺮآﯾﻨﺪ ﻗﺪم زدن ﺗﺼﺎدفی در پیشبینی ارزش در ﻣﻌﺮض رﯾﺴﮏ. مجله مهندسی مالی و مدیریت اوراق بهادار، 4(16)،92-75.
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12. زراء نژاد، منصور؛ رئوفی، علی (1394). پیشبینی بازار روزانه بورس اوراق بهادارتهران: ارزیابی و مقایسه روشهای خطی و غیرخطی. دوفصلنامه اقتصاد پولی، مالی (دانش و توسعه سابق) دوره جدید، 20(9)، 29-1.
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13. فتاحی، شهرام؛خانزادی، آزاده؛ نفیسی مقدم، مریم (1394). پیشبینی تلاطم بازده سهام در بورس اوراق بهادار تهران با استفاده از روش شبیهسازی MCMC و الگوریتم متروپلیس هستینگ. فصلنامه علمی پژوهشی دانش مالی تحلیل اوراق بهادار، 9(32)،94 -79.
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14. نبوی چاشمی، سید علی؛ مختاری نژاد، ماریا (1395). مقایسه مدلهای حرکت براونی و براونی کسری و گارچ در برآورد نوسانات بازده سهام. مجله مهندسی مالی و مدیریت اوراق بهادار،29(1)، 44-21.
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15. Azar, A. Momeny (2009), Statistics and its application in management, SAMT Press. Iran. (In Persian).
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16. Amanina, N.A, Safiih, L.M, & Anthea, D.A.D (2014) Bootstrap percentile in GARCH models: Study case on volatility of Kuala Lumpur Shariah Index (KLSI).Science and Engineerin, 928-931.
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17. Beste, H.B,&Ufuk, Beyaztas (2018). BLOCK BOOTSTRAP PREDICTION INTERVALS FOR GARCH PROCESSES.Department of Statistics Bartin University, Bartin, Turkey, 1-19.
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18. Beyaztas, B.H, Beyaztas, U, Bandyopadhyay, S,& Huang, W.M (2018). New and fast block bootstrap-based prediction intervals for GARCH (1,1) process with application to exchange rates. The Indian Journal of Statistics, 80(1), 168-194.
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19. Chen, B, Gel, Y.R, Balakrishna, N, & Abraham, B (2011). Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes. Journal of Forecasting,30(1), 51-71.
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20. Essaddam, N, Mnasri (2015). Event-study volatility and bootstrapping: an international study.Applied Economics Letters, 22(3), 209-213.
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21. Fathi & Shoghi (2015). Simulation of stochastic differential equation of geometric Brownian motion by quasi-Monte Carlo method and its application in prediction of total index of stock market and value at risk. Mathematical Sciences, 9(3), 115-125.
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22. Frimpong, J.M, Oteng-Abayie, E.F (2006). Modelling and forecasting volatility of returns on the Ghana stock exchange using GARCH models.Munich Personal RePEc Archive, 27(593),1-21.
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23. Hansen, P.R, Lunde (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)?Journal of applied econometrics, 20(7), 873-889.
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24. Hatemi-J, A, Irandoust (2011). The dynamic interaction between volatility and returns in the US stock market using leveraged bootstrap simulations. Research in International Business and Finance, 25(3), 329-334.
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25. Hwang, E, Shin, D.W (2013). Stationary bootstrap prediction intervals for GARCH (p, q). Communications for Statistical Applications and Methods, 20(1), 41-52.
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26. Luger, R (2012). Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations. Computational Statistics & Data Analysis, 56(11), 3198-3211.
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32
33. Varga, L, Zempleni (2012). Weighted bootstrap in GARCH models. arXiv preprint arXiv,Cornell University, New York.
33
ORIGINAL_ARTICLE
Comparative Comparison of Stock Price Volatility Estimation by Garch and Bootstrap Garch
Since volatility measurement plays an important role in risk assessment and uncertainty in financial markets, this study provides an appropriate method for predicting stock pricefluctuations using the GARCH and Bootstrap Garch method. And then compare the confidence intervals by the two methods. The research data were collected by reviewing the statistics of the companies listed in the list of the top 50 companies in the securities market. The results show that the confidence interval of the Bootstrap Garch method is shorter than the Garch method,so the Bootstrap Garch method provides a more accurate prediction than the GARCH method. In addition, it is usually expected to increase with the increase in horizons of prediction of variance, but this does not occur for the Garch (1.1) method; therefore, it seems that the prediction of the variance of the Bootstrap GARCH model has more compatibility with theoretical evidence.
https://jamm.scu.ac.ir/article_16666_b70c5227fc6575ebce74dda214db8cec.pdf
2021-04-21
169
194
10.22055/jamm.2020.32338.1794
Confidence interval
Bootstrap
GARCH
Volatility
Rahim
Ghasemiyeh
r.ghasemiyeh@scu.ac.ir
1
Department of Management,, Faculty of Economic and Social Sciences, Shahid Chamran University of Ahvaz,, Ahvaz, Iran
LEAD_AUTHOR
Hasanali
Sinaei
ha.sinaei11@gmail.com
2
Department of Management,, Faculty of Economic and Social Sciences, Shahid Chamran University of Ahvaz,, Ahvaz, Iran
AUTHOR
abdolhosein
Neysi
aneysi@sci.ac.ir
3
Department of Management,, Faculty of Economic and Social Sciences, Shahid Chamran University of Ahvaz,, Ahvaz, Iran
AUTHOR
Zahra
chaharlangi sardarabadi
zahrachaharlangi1371@yahoo.com
4
Department of Management,, Faculty of Economic and Social Sciences, Shahid Chamran University of Ahvaz,, Ahvaz, Iran
AUTHOR
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