Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces

This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a C0-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results.