1. Adams, C.R. The general theory of a class of linear partial q- difference equations, Trans. Am. Math. Soc. 26 (1924), 283–312.
2. Adams, C.R. Note on the integro-q-difference equations, Trans. Am. Math. Soc. 31 (4) (1929), 861–867.
3. Agarwal, R.P. Certain fractional q-integrals and q-derivatives, Proceedings of the Cambridge Philosophical Society 66 (1969), 365–370.
4. Agarwal, R.P., Belmekki, M. and Benchohra, M. A survey on semi- linear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Differ. Equ. 2009, 981728 (2009).
5. Ahmad, B. and Nieto, J.J. Riemann-Liouville fractional integro- differential equations with fractional nonlocal integral boundary conditions, Bound. Value Probl. 2011, 2011:36, 9 pp.
6. Ahmad B. and Ntouyas, S.K. Existence of solutions for nonlinear fractional q-difference inclusions with nonlocal robin (separated) conditions, Mediterr. J. Math. 10 (2013), 1333–1351.
7. Ahmad B. and Ntouyas, S.K. Boundary value problem for fractional differential inclusions with four-point integral boundary conditions, Surv. Math. Appl. 6 (2011), 175–193.
8. Amini-Harandi, A. Endpoints of set-valued contractions in metric spaces, Nonlinear Anal. 72 (2010), 132–134.
9. Anastassiou, G.A. Principles of delta fractional calculus on time scales and inequalities, Math. Comput. Modelling 52 (2010), 556–566.
10. Annaby, M.H. and Mansour, Z.S. q-fractional calculus and equations, With a foreword by Mourad Ismail. Lecture Notes in Mathematics, 2056. Springer, Heidelberg, 2012.
11. Atici, F. and Eloe, P.W. Fractional q-calculus on a time scale, J. Non linear Math. Phys. 14 (2007), 333–344.
12. Aubin, J. and Ceuina, A. Differential inclusions: set-valued maps and viability theory, Springer-Verlag, 1984.
13. Baleanu, D., Agarwal, R. P., Mohammadi, H. and Rezapour, S. Some existence results for a nonlinear fractional differential equation on partially ordered banach spaces, Bound. Value Probl. 2013 (2013), 112 pp.
14. Bohner M. and Peteson, A. Dynamic equations on time scales, Birkhauser, Boston, 2001.
15. Carmichael, R.D. The general theory of linear q-difference equations, Amer. J. Math. 34 (1912), 147–168.
16. Deimling, K. Multi-valued differential equations, Walter de Gruyter, Berlin, 1992.
17. Ferreira, R.A.C. Nontrivials solutions for fractional q-difference boundary value problems, Electron. J. Qual. Theory Differ. Equ. 2010, No. 70, 10 pp.
18. Gasper, G.and Rahman, M. Basi hypergeometric series, University Press, Cambridge, 1990.
19. Granas, A. and Dugundji, J. Fixed point theory, Springer-Verlag, 2005.
20. Hedayati, V. and Samei, M.E. Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous Dirichlet boundary conditions, Bound. Value Probl. 2019 (2019), 163 pp.
21. Hilfer, R. Applications of fractional calculus in physics, World Scientific, 2000.
22. Jackson, F.H. On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh 46 (1909), 253–281.
23. Jackson, F.H. On q-definite integrals, Pure Appl. Math. Q. 41 (1910), 193–203.
24. Jackson, F.H. q-difference equations, Am. J. Math. 32 (1910), 305–314.
25. Kac, V. and Cheung, P. Quantum calculus, Universitext, Springer, New York, 2002.
26. Kilbas, A.A., Srivastava, H. M. and Trujillo, J.J. Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science, North-Holland, 2006.
27. Kisielewicz, M. Differential inclusions and optimal control, Kluwer, Dordrecht, 1991.
28. Mason, T.E. On properties of the solution of linear q-difference equations with entire function coefficients, Am. J. Math. 37 (1915), 439–444.
29. Ntouyas, S.K. and Samei, M.E. Existence and uniqueness of solutions for multi-term fractional q-integro-differential equations via quantum calculus Adv. Difference Equ. 2019, Paper No. 475, 20 pp.
30. Phung, P. D. and Truong, L. X. On a fractional differential inclusion with integral boundary conditions in Banach space, Fract. Calc. Appl. Anal. 16(2013), 538–558.
31. Podlubny, I. Fractional differential equations, Academic Press, 1999.
32. Rajković, P. M., Marinković, S. D. and Stanković, M. S. Fractional in tegrals and derivatives in q-calculus,Appl. Anal. Discrete Math. 1 (2007), 311–323.
33. Rezapour, Sh. and Hedayati, V. On a Caputo fractional differential inclusion with integral boundary condition for convex-compact and nonconvex- compact valued multifunctions,Kragujev. J. Math. 41 (1)(2017), 143–158.
34. Samei, M.E. Existence of solutions for a system of singular sum fractional q-differential equations via quantum calculus, Adv. Differ. Equ. 2020(2020), 23.
35. Samei, M.E., Hedayati, V. and Rezapour, Sh. Existence results for a fraction hybrid differential inclusion with Caputo–Hadamard type fractionalderivative, Adv. Difference Equ. 2019, Paper No. 163, 15 pp.
36. Samei, M.E. and Khalilzadeh Ranjbar, G. Some theorems of existence of solutions for fractional hybrid q-difference inclusion, J. Adv. Math. Stud. 12 (2019), 63–76.
37. Samei, M.E., Ranjbar,G.K. and Hedayati, V. Existence of solutions for equations and inclusions of multi-term fractional q-integro-differential with non-separated and initial boundary conditions, J. Inequal. Appl. 2019
(2019), 273.
38. Samko, S.G. ,Kilbas, A.A. and Marichev, O.I. Fractional integrals and es: Theory and applications, Gordon and Breach Science Publishers, Switzerland; Philadelphia, Pa., USA, 1993.
39. Trjitzinsky, W.J. Analytic theory of linear q-difference equations, ActaMath. 61 (1933), 1–3840. Wang, J. and Ibrahim, A.G. Existence and controllability results for nonlocal fractional impulsive differential inclusions in Banach spaces, Journalof Function Spaces and Applications, 2013, Article ID 518306, 16 pp.actional integrals and
40. Wang, J. and Ibrahim, A.G. Existence and controllability results for nonlocal fractional impulsive differential inclusions in Banach spaces, Journalof Function Spaces and Applications, 2013, Article ID 518306, 16 pp.
Send comment about this article