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

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 instanta...

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Bibliographic Details
Published in:	AIMS mathematics Vol. 8; no. 5; pp. 11752 - 11780
Main Authors:	Nuwairan, Muneerah Al, Ibrahim, Ahmed Gamal
Format:	Journal Article
Language:	English
Published:	AIMS Press 01.01.2023
Subjects:	atangana-baleanu fractional derivative fractional differential inclusions instantaneous and noninstantaneous impulses measure of noncompactness
ISSN:	2473-6988, 2473-6988
Online Access:	Get full text
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Summary:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2023595