Existence of $ S $-asymptotically $ \omega $-periodic solutions for non-instantaneous impulsive semilinear differential equations and inclusions of fractional order $ 1 < \alpha

Existence of $ S $-asymptotically $ \omega $-periodic solutions for non-instantaneous impulsive semilinear differential equations and inclusions of fractional order $ 1 < \alpha < 2 $

Published:2023 Issue:1 Volume:8 Page:76-101
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Alsheekhhussain Zainab¹,Ibrahim Ahmed Gamal²,Ramadan Rabie A.¹³

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Ha'il, Hail Saudi Arabia

2. Department of Mathematics, College of Sciences, King Faisal University, Saudi Arabia

3. Cairo University, Department of Computer Engineering, Faculty of Engineering, Cairo, 12613, Egypt

Abstract

<abstract><p>It is known that there is no non-constant periodic solutions on a closed bounded interval for differential equations with fractional order. Therefore, many researchers investigate the existence of asymptotically periodic solution for differential equations with fractional order. In this paper, we demonstrate the existence and uniqueness of the $ S $-asymptotically $ \omega $-periodic mild solution to non-instantaneous impulsive semilinear differential equations of order $ 1 < \alpha < 2 $, and its linear part is an infinitesimal generator of a strongly continuous cosine family of bounded linear operators. In addition, we consider the case of differential inclusion. Examples are given to illustrate the applicability of our results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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