A Filippov's Theorem and Topological Structure of Solution Sets for Fractional q-Difference Inclusions

Abstract

In this paper we present some existence results and topological structure of the solution set for a class of Caputo implicit fractional q-difference inclusions in Banach spaces. Firstly, using the set-valued analysis, we study some global existence results and we present a new version of Filippov's Theorem. Further, we obtain results in the cases where the nonlinearity is upper as well as lower semi-continuous with respect to the second argument by using Mnch's and Schauder-Tikhonov fixed point theorems and the concept of measure of noncompactness. In the last section, we illustrate our results by an example.

Topics & Concepts