Abdelkrim Salim, Said Abbas, Mouffak Benchohra, and Erdal Karapinar
A Filippov’s Theorem and Topological Structure of Solution Sets for Fractional q-Difference Inclusions
Dynamic Systems and Applications 31 (2022) 17-34

https://doi.org/10.46719/dsa202231.01.02

ABSTRACT.
In this paper we present some existence results and topological structure of the solution set for a class of Caputo 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 Monch’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.

AMS (MOS) Subject Classification. 26A33, 34A60.
Key Words and Phrases. Fractional q-difference inclusion, compactness, measure of noncompactness, solution set, topological structure, fixed point, multifunction, measurable selection.