Topological Structure of Solution Set to a Fractional Differential Inclusion Problem with Delay

Abstract

In this paper, we investigate the topological structure of the solution set to a fractional differential inclusion with delay defined on the half-line. We first prove that the solution set to the inclusion is an Rδ-set on compact intervals. Then, by means of the inverse limit method, we generalize our results to noncompact intervals. Moreover, under convex and nonconvex conditions, an Rδ-property solution set is obtained for some nonlocal problems, where the nonlocal function is set-valued. Further, we study the symmetry of the solution set under some conditions.