Nonlocal impulsive differential equations and inclusions involving Atangana-Baleanu fractional derivative in infinite dimensional spaces-Reference-Cited by-同舟云学术

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

Published:2023 Issue:5 Volume:8 Page:11752-11780
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Nuwairan Muneerah Al¹,Ibrahim Ahmed Gamal²

Affiliation:

1. Department of Mathematics, College of Sciences, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia

2. Department of Mathematics, College of Sciences, Cairo University, Egypt

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference48 articles.

1. Z. Agur, L. Cojocaru, G. Mazor, R. M. Anderson, Y. L. Danon, Pulse mass measlesvaccination across age cohorts, Proc. Natl. Acad. Sci. U. S. A., 90 (1993), 11698–11702. http://doi.org/10.1073/pnas.90.24.11698

2. X. Z. Liu, G. Ballinger, Boundedness for impulsive delaydifferential equations and applications in populations growth models, Nonlinear Anal., 53 (2003), 1041–1062. http://doi.org/10.1016/S0362-546X(03)00041-5

3. M. Benchohra, J. Henderson, S. Ntouyas, Impulsive differential equations and inclusions, Hindawi Publishing Corporation, 2007.

4. J. R. Wang, M. Fečkan, Non-instantaneous impulsive differential equations: basic theory and computation, IOP Publishing Ltd, 2018.

5. R. Agarwal, S. Hristova, D. O'Regan, Non-instantaneous impulses in differential equations, Springer, 2017.

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