1] Agarwal, R. P., 1969. Certain fractional q-integrals and q-derivatives. Mathematical Proceedings of the Cambridge Philosophical Society, 66, pp. 365–370. doi: 10.1017/S0305004100045060
[2] Ahmad, B., Tariboon, J., Ntouyas, S. K., Alsulami, H. H. and Monaquel, S., 2016. Existence results
for impulsive fractional q-difference equations with anti-periodic boundary conditions, Boundary
Value Problems, 2016, pp. 15. doi: 10.1186/s13661-016-0521-y
[3] Ahmadi, A. and Samei, M. E., 2020. On existence and uniqueness of solutions for a class of coupled system of three term fractional q-differential equations, Journal of Advanced Mathematical Studies, 14(1), pp. 69–80.
[4] Al-Salam, W. A., 1966. Some fractional q-integrals and q-derivatives, Proceedings of the Edinburgh Mathematical Society, 15, pp. 135–140. doi: 10.1017/S0013091500011469
[5] Annaby, M. H. and Mansour, Z. S., 2012. q-Fractional Calculus and Equations. Heidelberg, New York, Springer.
[6] Berhail, A., Tabouche, N., Alzabut, J. and Samei, M. E., 2022. Using Hilfer-Katugampola fractional derivative in initial value Mathieu fractional differential equations with application on particle in the plane, Advances in Continuous and Discrete Models: Theory and Applications, 2022, pp. 44. doi:10.1186/s13662-022-03716-6
[7] Boutiara, A., Kaabar, M. K. A., Siri, Z., Samei, M. E. and Yue, X. G., 2022. Investigation of a generalized proportional Langevin and Sturm-Liouville fractional differential equations via variable coefficients and anti-periodic boundary conditions with a control theory application arising from complex networks, Mathematical Problems in Engineering, 2022, pp. 21 pages. doi: 10.1155/2022/7018170
[8] Eswari, R., Alzabut, J. and Samei, M. E., Tunç, C. and Jonnalagad, J. M., 2022. New results on the
existence of periodic solutions for Rayleigh equations with state-dependent delay, Nonautonomous Dynamical Systems, 9, pp. 103–115. doi: 10.1515/msds-2022-0149
[9] Hedayati, V. and Samei, M. E., 2019. Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous Dirichlet boundary conditions, Boundary Value Problems, 2019, pp. 141. doi: 10.1186/s13661-019-1251-8
[10] Hilfer, R., 2000. Applications of Fractional Calculus in Physics, Singapore, World Scientific.
[11] Houas, M. and Samei, M. E., 2022. Existence and Mittag-Leffler-Ulam-stability results for duffing type problem involving sequential fractional derivatives, International Journal of Applied and Computational Mathematics, 8, pp. 185. doi: 10.1007/s40819-022-01398-y
[12] Houas, M. and Samei, M. E., 2023. Existence and stability of solutions for linear and nonlinear damping of q−fractional Duffing-Rayleigh problem, Mediterranean Journal of Mathematics, 20, pp. 148. doi: 10.1007/s00009-023-02355-9
[13] Izadi, M. and Samei, M. E., 2022. Time accurate solution to Benjamin-Bona-Mahony Burgers equation via Taylor-Boubaker series scheme, Boundary Value Problems, 2022, pp. 17.doi:10.1186/s13661-022-01598-x
[14] Jackson, F. H., 1910. q-difference equations, American Journal of Mathematic, 32(4), pp. 305–314.doi: 10.2307/2370183
[15] Mishra, S. K., Rajković, P., Samei, M. E., Chakraborty, S. K., Ram, B. and Kaabar, M. K. A., 2021. A
q-gradient descent algorithm with quasi-Fejér convergence for unconstrained optimization problems, Fractal and Fractional, 5(3), pp. 110. doi: 10.3390/fractalfract5030110
[16] Ntouyas, S. K., and M. E. Samei, 2019. Existence and uniqueness of solutions for multi-term fractional q-integro-differential equations via quantum calculus, Advances in Difference Equations, 2019, pp. 475. doi: 10.1186/s13662-019-2414-8
[17] Samei, M. E., Hedayati, V. and Rezapour, S., 2019. Existence results for a fraction hybrid differential inclusion with Caputo-Hadamard type fractional derivative, Advances in Difference Equations, 2019,
pp. 163. doi: 10.1186/s13662-019-2090-8
[18] Samei, M. E., Karimi, L. and Kaabar, M. K. A., 2022. To investigate a class of multi-singular pointwise defined fractional q-integro-differential equation with applications, AIMS Mathematics, 7(5),pp. 7781–7816. doi: 10.3934/math.2022437
[19] Suantai, S., Ntouyas, S. K., Asawasamrit, S. and Tariboon, J., 2015. A coupled system of fractional q-integro-difference equations with nonlocal fractional q-integral boundary conditions, Advances in Difference Equations, 2015, pp. 124. doi: 10.1186/s13662-015-0462-2
[20] Subramanian, M., Alzabut, J., Dumitru, D., Samei, M. E. and Zadaf, A., 2021. Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions, Advances in Difference Equations, 2021, pp. 267. doi: 10.1186/s13662-021-03414-9
[21] Tariboon, J. and Ntouyas, S. K., 2013. Quantum calculus on finite intervals and applications to impulsive difference equations, Advances in Difference Equations, 2013, 282. doi: 10.1186/1687- 1847-2013-282
[22] Tariboon, J., and Ntouyas, S. K. and Agarwal, P., 2015. New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations, Advances in Difference Equations, 2015, pp. 18. doi: 10.1186/s13662-014-0348-8
)