Optimal Control of Clarke Subdifferential Type Fractional Differential Inclusion with Non-instantaneous Impulses Driven by Poisson Jumps and Its Topological Properties

Abstract

This article is devoted to studying the topological structure of a solution set for Clarke subdifferential type fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps. Initially, for proving the solvability result, we use a nonlinear alternative of Leray–Schauder fixed point theorem, Gronwall inequality, stochastic analysis, a measure of noncompactness, and the multivalued analysis. Furthermore, the mild solution set for the proposed problem is demonstrated with nonemptyness, compactness, and, moreover, $$R_\delta $$ -set. By employing Balder’s theorem, the existence of optimal control is derived. At last, an application is provided to validate the developed theoretical results.