Topology structure of solution set of fractional non-autonomous evolution inclusions

This paper investigates the topological characteristics of the set of solutions to non-autonomous fractional evolution inclusions. We present the concept of mild solutions for nonautonomous fractional evolution inclusions and prove that the solution set is nonempty and compact. Moreover, when the space is a reflexive Banach space, we demonstrate that the solution set is an R_{\delta} -set, indicating that it may not be a single entity.