Existence of Solutions for Fractional Differential Inclusions with Initial Value Condition and Non-instantaneous Impulses

Abstract

In this paper, we mainly consider the existence of solutions for a kind of ψ -Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.