Nonlocal impulsive differential equations and inclusions involving Atangana-Baleanu fractional derivative in infinite dimensional spaces

Abstract

The aim of this paper is to derive conditions under which the solution set of a non-local impulsive differential inclusions involving Atangana-Baleanu fractional derivative is a nonempty compact set in an infinite dimensional Banach spaces. Existence results for solutions in the presence of instantaneous or non-instantaneous impulsive effect are given. We considered the case where the right hand side is either a single valued function, or a multifunction. This generalizes recent results to the case when there are impulses, the right hand side is a multifunction, and where the dimension of the space is infinite. Examples are given to illustrate the effectiveness of the established results.

Keywords

• atangana-baleanu fractional derivative
• fractional differential inclusions
• instantaneous and noninstantaneous impulses
• measure of noncompactness