An existence result for a new class of fuzzy fractional differential inclusions with Clarke's subdifferential via resolvent operators in Banach spaces

Abstract

The purpose of this article is to establish a new result on the existence of a solution for a new class of fuzzy fractional differential inclusions with Clarke's subdifferential via the resolvent operator in Banach spaces. First, we introduce a new class of fuzzy fractional differential inclusions with Clarke's subdifferential via the resolvent operator in Banach spaces. Then, we establish existence conditions for this inclusion system using Bohnenblust-Karlin's fixed point theorem under some suitable conditions. Finally, we give an example to illustrate the main results. Our results are new even when applied to the corresponding fractional differential inclusions in the literature.