References
- C.R. Adams. On the linear ordinary q-difference equation. Ann. of Math., 30: 195–205, 1928. http://dx.doi.org/10.2307/1968274.
- B. Ahmad. Boundary value problems for nonlinear third-order q-difference equations. Electron. J. Differential Equations, 94: 1–7, 2011.
- B. Ahmad, A. Alsaedi and S.K. Ntouyas. 2012 A study of second-order q-difference equations with boundary conditions. Adv. Difference Equ., 35: 1–10, 2012.
- B. Ahmad and J.J. Nieto. Basic theory of nonlinear third-order q-difference equations and inclusions. Math. Model. Anal., 18: 122–135, 2013. http://dx.doi.org/10.3846/13926292.2013.760012.
- B. Ahmad and S.K. Ntouyas. Boundary value problems for q-difference inclusions. Abstr. Appl. Anal., 1–15: 2011.
- M.H. Annaby and Z.S. Mansour q-taylor and interpolation series for jackson q-difference operators. J. Math. Anal. Appl., 344: 472–483, 2008. http://dx.doi.org/10.1016/j.jmaa.2008.02.033.
- M.H. Annaby and Z.S. Mansour. q-Fractional Calculus and Equations, volume 2056 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2012.
- G. Bangerezako. Variational q-calculus. J. Math. Anal. Appl., 289: 650–665, 2004. http://dx.doi.org/10.1016/j.jmaa.2003.09.004.
- L. Byszewski. Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl., 162: 494–505, 1991. http://dx.doi.org/10.1016/0022-247X(91)90164-U.
- L. Byszewski and V. Lakshmikantham. Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Appl. Anal., 40: 11–19, 1991. http://dx.doi.org/10.1080/00036819008839989.
- R.D. Carmichael. The general theory of linear q-difference equations. Amer. J. Math., 34: 147–168, 1912. http://dx.doi.org/10.2307/2369887.
- K. Deimling. Multivalued Differential Equations. Walter De Gruyter, Berlin, New York, 1992.
- A. Dobrogowska and A. Odzijewicz. Second order q-difference equations solvable by factorization method. J. Comput. Appl. Math., 193: 319–346, 2006. http://dx.doi.org/10.1016/j.cam.2005.06.009.
- M. El-Shahed and H. A. Hassan. Positive solutions of q-difference equation. Proc. Amer. Math. Soc., 138: 1733–1738, 2010. http://dx.doi.org/10.1090/S0002-9939-09-10185-5.
- T. Ernst. The history of q-calculus and a new method. UUDMReport2000:16. Department of Mathematics, Uppsala University, 2000.
- R. Ferreira. Nontrivial solutions for fractional q-difference boundary value problems. Electron. J. Qual. Theory Differ. Equ., 70: 1–10, 2010.
- G. Gasper and M. Rahman. Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990.
- G. Gasper and M. Rahman. Some systems of multivariable orthogonal q-Racah polynomials. Ramanujan J., 13: 389–405, 2007. http://dx.doi.org/10.1007/s11139-006-0259-8.
- A. Granas and J. Dugundji. Fixed Point Theory. Springer-Verlag, New York, 2005.
- Sh. Hu and N. Papageorgiou. Handbook of Multivalued Analysis, Theory I. Kluwer, Dordrecht, 1997.
- M.E.H. Ismail and P. Simeonov. q-difference operators for orthogonal polynomials. J. Comput. Appl. Math., 233: 749–761, 2009. http://dx.doi.org/10.1016/j.cam.2009.02.044.
- F.H. Jackson. On q-functions and a certain difference operator. Trans. Roy. Soc. Edinburgh, 46: 253–281, 1908. http://dx.doi.org/10.1017/S0080456800002751.
- F.H. Jackson. On q-difference equations. Amer. J. Math., 32: 305–314, 1910. http://dx.doi.org/10.2307/2370183.
- V. Kac and P. Cheung. Quantum Calculus. Springer, New York, 2002.
- A. Lasota and Z. Opial. An application of the kakutani-ky fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13: 781–786, 1965.
- J. Ma and J. Yang. Existence of solutions for multi-point boundary value problem of fractional q-difference equation. Electron. J. Qual. Theory Differ. Equ., 92: 1–10, 2011.
- T.E. Mason. On properties of the solutions of linear q-difference equations with entire function coefficients. Amer. J. Math., 37: 439–444, 1915. http://dx.doi.org/10.2307/2370216.
- D. O'Regan. Fixed-point theory for the sum of two operators. Appl. Math. Lett., 9: 1–8, 1996. http://dx.doi.org/10.1016/0893-9659(95)00093-3.
- W.V. Petryshyn and P.M. Fitzpatric. A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact maps. Trans. Amer. Math. Soc., 194: 1–25, 1974. http://dx.doi.org/10.1090/S0002-9947-1974-2478129-5.