Existence Results for Fractional Differential Inclusions Involving Non-Convex Valued Maps with Four-Point Nonlocal Integral Boundary Conditions

Abstract

This paper studies the existence of solutions for fractional differential inclusions of order $q \in (1,2]$ with four-point nonlocal integral boundary conditions. We consider two cases: (a) the multivalued map in the problem is not necessarily convex valued, (b) the multivalued map consists of non-convex values. A nonlinear alternative of Leray Schauder type coupled with the selection theorem of Bressan and Colombo is employed to deal with the first case, while the second case is based on Wegrzyk's fixed point theorem for generalized contractions.