Existence results for fractional semilinear differential inclusions in Banach spaces

Abstract

We consider the existence of mild solutions for fractional semilinear differential inclusions involving a nonconvex set-valued map in Banach spaces. First, we study the continuous property of the solution map for an auxiliary fractional differential equation. Then the main result is obtained by using this solution map, selection theorems from multivalued analysis and Schauder’s fixed point theorem. Finally an example to illustrate the applications of the main result is also given.