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Fractal Fract
Volume 10
Issue 6
10.3390/fractalfract10060366
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Article

Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces

by
Zainab Alsheekhhussain
1,*,
Ahmed Gamal Ibrahim
2,
Mohammed Mossa Al-Sawalha
1 and
Marwa Ennaceur
1
1
Department of Mathematics, Faculty of Science, University of Ha’il, Hai’l 55476, Saudi Arabia
2
Department of Mathematics Al-Ahsa, College of Science, King Fiasal University, Hofuf 36362, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(6), 366; https://doi.org/10.3390/fractalfract10060366
Submission received: 17 February 2026 / Revised: 20 May 2026 / Accepted: 21 May 2026 / Published: 28 May 2026
(This article belongs to the Special Issue Fractal Functions: Theoretical Research and Application Analysis)
Versions Notes

Abstract

This paper examines the sufficient conditions that guarantee the existence of solutions and anti-periodic solutions to five classes of fractional differential equations and inclusions involving the weighted generalized Atangana–Baleanu differential operator of order δ∈(1,2) under non-local conditions and with instantaneous or non-instantaneous impulses in Banach spaces whose dimension is infinite. First, we deduce some novel properties of this differential operator, then derive the formula for the solutions and anti-periodic solutions, and investigate their existence for the problems presented. Our method relies on certain properties of the Atangana–Baleanu differential operator, which we will obtain, as well as the fixed-point theorems that can be applied to the functions and multi-valued functions. Our work generalizes recently published results. In the final section, we present some examples to illustrate how our theoretical results can be applied.
Keywords: fractional differential equations and inclusions; weighted generalized Atangana–Baleanu fractional derivative; instantaneous and non-instantaneous impulses; solutions and anti-periodic solutions; measure of noncompactness. fractional differential equations and inclusions; weighted generalized Atangana–Baleanu fractional derivative; instantaneous and non-instantaneous impulses; solutions and anti-periodic solutions; measure of noncompactness.

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MDPI and ACS Style

Alsheekhhussain, Z.; Ibrahim, A.G.; Al-Sawalha, M.M.; Ennaceur, M. Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces. Fractal Fract. 2026, 10, 366. https://doi.org/10.3390/fractalfract10060366

AMA Style

Alsheekhhussain Z, Ibrahim AG, Al-Sawalha MM, Ennaceur M. Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces. Fractal and Fractional. 2026; 10(6):366. https://doi.org/10.3390/fractalfract10060366

Chicago/Turabian Style

Alsheekhhussain, Zainab, Ahmed Gamal Ibrahim, Mohammed Mossa Al-Sawalha, and Marwa Ennaceur. 2026. "Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces" Fractal and Fractional 10, no. 6: 366. https://doi.org/10.3390/fractalfract10060366

APA Style

Alsheekhhussain, Z., Ibrahim, A. G., Al-Sawalha, M. M., & Ennaceur, M. (2026). Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces. Fractal and Fractional, 10(6), 366. https://doi.org/10.3390/fractalfract10060366

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