D. A. Benson, R. Schumer, M. M. Meerschaert and S. W. Wheatcraft, Fractional Dispersion Levy
Motion and the MADE Tracer Tests, Transport in Porous Media, 42(2001), 211–240.
 A. Benson, W. David, Stephen Wheatcraft and Mark M. Meerschaert, The fractional-order governing
equation of Levy motion, Water resources research, 36(2000), 1413-1423.
 V. Gafiychuk, B. Datsko and V. Meleshko, Mathematical modeling of time fractional reactiondiffusion
systems, Journal of Computational and Applied Mathematics, 220(2008), 215-225.
 R. Hilfer, Applications of fractional calculus in physics, Singapore: World Scientific. 2000.
 R. L. Magin, Fractional calculus in bioengineering, New York: Begell., 2021.
 K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations,
New York, NY: Wiley., 1993.
 O. Bavi, M. Hosseininia, M. Heydari and N. Bavi, SARS-CoV-2 rate of spread in and across tissue,
groundwater and soil: A meshless algorithm for the fractional diffusion equation, Engineering Analysis
with Boundary Elements, 138 (2022), 108–117.
 S. Traytak, The use of fractional-order derivatives for determination of the time-dependent rate constant,
Chemical Physics Letters, 173(1990), 63-66.
 C. Friedrich, H. Schiesse and A. Blumen, Constitutive behavior modeling and fractional derivatives,
Rheology Series, 8(1999), 429-466.
 K. A. Diethelm, A fractional calculus based model for the simulation of an outbreak of Dengue fever,
Nonlinear Dyn. 71(2013), 613-619.
 L. Vinnett, M. Alvarez-Silva, A. Jaques, F. Hinojosa, and J. Yianatos, Batch flotation kinetics: Fractional
calculus approach, Minerals Engineering, 77(2015), 167-171.
 S. Abo-Dahab, A. Kilany, E. A. Abdel-Salam and A. Hatem, Fractional derivative order analysis and
temperature-dependent properties on p- and SV-waves reflection under initial stress and three-phaselag
model, Results in Physics, 18(2020), 103-270.
 E. El-Zahar, A. Alotaibi, A. Ebaid, A. Aljohani and J. G. Aguilar, The Riemann–Liouville fractional
derivative for Ambartsumian equation, Results in Physics, 19(2020), 103-551.
 S. Butera and M. D. Paola, A physically based connection between fractional calculus and fractal
geometry, Annals of Physics, 350(2014), 146-158.
 N. Faraz, M. Sadaf, G. Akram, I. Zainab and Y. Khan, Effects of fractional order time derivative
on the solitary wave dynamics of the generalized ZK–Burgers equation, Results in Physics, 25(2021),
 X. Li and P. J. Wong, High order approximation to new generalized Caputo fractional derivatives and
its applications, Journal of Computational Physics, 281(2018), 787-805.
 W. Tian, H. Zhou and W. Deng, A class of second order difference approximations for solving space
fractional diffusion equations, Mathematics of Computation, 84(2015), 1703-1727.
 Z. Hao and W. Cao, An Improved Algorithm Based on Finite Difference Schemes for Fractional
Boundary Value Problems with Nonsmooth Solution, Journal of Scientific Computing, 73(2017), 395-
 H. Wang and T. S. Basu, A Fast Finite Difference Method for Two-Dimensional Space-Fractional
Diffusion Equations, SIAM Journal on Scientific Computing, 34 (5) (2012) , A2444-A2458.
 Z. Hao, M. Park, G. Lin and Z. Cai, Finite Element Method for Two-Sided Fractional Differential
Equations with Variable Coefficients: Galerkin Approach, Journal of Scientific Computing, 79(2018),
 W. Zeng, A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation
with Nonsmooth Solution, East Asian Journal on Applied Mathematics, 10(2020), 89-105.
 M. Habibli and M. Noori Skandari, Fractional Chebyshev pseudospectral method for fractional optimal
control problems, Optimal Control Applications and Methods, 40(3) (2019), 558–572.
 Y. Huang, F. Mohammadi Zadeh, M. Hadi Noori Skandari, H. Ahsani Tehrani and E .Tohidi, Space–
time Chebyshev spectral collocation method for nonlinear time‐fractional Burgers equations based on
efficient basis functions, Mathematical Methods in the Applied Sciences, 44(5) (2020), 4117–4136.
 N. Peykrayegan, M. Ghovatmand and M. H. Noori Skandari, On the convergence of Jacobi‐Gauss
collocation method for linear fractional delay differential equations, Mathematical Methods in the
Applied Sciences, 44(2) (2020), 2237–2253.
 N. Peykrayegan, M. Ghovatmand and M. H. N. Skandari, An efficient method for linear fractional
delay integro-differential equations. Computational and Applied Mathematics, 40(7)(2021).
 P. Xiaobing, X. Yang, M. H. Noori Skandari, E. Tohidi and S. Shateyi, A new high accurate approximate
approach to solve optimal control problems of fractional order via efficient basis functions.
Alexandria Engineering Journal, 61(8)(2022), 5805–5818.
 Y. Yang and H. M. Noori Skandari, Pseudospectral method for fractional infinite horizon optimal
control problems. Optimal Control Applications and Methods, 41(6)(2020), 2201–2212.
 Y. Zhang, X. Liu, M. R. Belić, W. Zhong, Y. Zhang and M. Xiao, Propagation Dynamics of a Light
Beam in a Fractional Schrödinger Equation, Physical Review Letters, 115(18)(2015), 180403.
 D. del Castillo-Negrete and L. Chac on, Parallel heat transport in integrable and chaotic magnetic
fields, Phys. Plasmas, 19(5) (2012), 056112.
 Y. Zhang, M. M. Meerschaert and R. M. Neupauer, Backward fractional advection dispersion model
for contaminant source prediction, Water Resour. Res., 52(2016), 2462–2473.
 L. P lociniczak, Analytical studies of a time-fractional porous medium equation. Derivation, approximation
and applications, Commun. Nonlinear Sci. Numer. Simul., 24(2015), 169–183.
 R. Metzler, J. H. Jeon, A. G. Cherstvy and E. Barkai, Anomalous diffusion models and their properties:
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Phys.
Chem. Chem. Phys., 16(2014), 24128–24164.
 M. Yamamoto, Asymptotic expansion of solutions to the dissipative equation with fractional Laplacian,
SIAM J. Math. Anal., 44(2012), 3786–3805.
 P. Constantin and J. Wu, Behavior of solutions of 2D Quasi-geostrophic equations, SIAM J. Math.
Anal., 30(1999), 937–948.
 A. de Pablo, F. Quirós, A. Rodrıguez, & J. L. Vazquez, A fractional porous medium equation, Adv.
Math., 226(2011), 1378–1409.
 S. Duo, L. Ju and Y. Zhang, A fast algorithm for solving the space–time fractional diffusion equation.
Computers & Mathematics with Applications, 75(6)(2018), 1929–1941.
 H. Ye, F. Liu, V. Anh and I. Turner, Maximum principle and numerical method for the multi-term
time–space Riesz–Caputo fractional differential equations, Applied Mathematics and Computation,
227 (2014), 531-540.
 M. Stynes, E. Oriordan and J. L. Gracia, Error Analysis of a Finite Difference Method on Graded
Meshes for a Time-Fractional Diffusion Equation, SIAM Journal on Numerical Analysis, 55(2017),
 C. Li and F. Zeng, Numerical methods for fractional calculus, Boca Raton, FL: CRC Press, Taylor &
Francis Group, 2015.
 M. Chen, W. Deng and Y. Wu, Superlinearly convergent algorithms for the two-dimensional spacetime
Caputo-Riesz fractional diffusion equation, Applied Numerical Mathematics, 70(2013), 22-41.