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Received April 4, 2020; Accepted June 28, 2020; Published July 7, 2020
Abstract. We prove the existence of solutions for fractional differential inclusions containing right-Caputo and left-Riemann-Liouville fractional derivatives of different orders and right-left Riemann-Liouville fractional integrals, supplemented with nonlocal boundary conditions. Our first existence result dealing with the convex valued maps involved in the given problem is derived by applying the nonlinear alternative of Leray-schauder type. We apply Wegrzyk’s fixed point theorem to prove our second result, which is concerned with the generalized contraction (nonconvex valued) maps. We also discuss the dimension of the solution set.
How to Cite this Article:
Ahmed Alsaedi, Abrar Broom, Sotiris K. Ntouyas, Bashir Ahmad, Existence results and the dimension of the solution set for a nonlocal inclusions problem with mixed fractional derivatives and integrals, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 28, pp. 1-15.