ArticleOpen Access

EXISTENCE AND STABILITY OF SOLUTION IN BANACH SPACE FOR AN IMPULSIVE SYSTEM INVOLVING ATANGANA–BALEANU AND CAPUTO–FABRIZIO DERIVATIVES

WADHAH AL-SADI

https://orcid.org/0000-0002-8284-8026

School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, P. R. China

E-mail Address: waddah27@gmail.com

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ZHOUCHAO WEI

https://orcid.org/0000-0001-6981-748X

School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, P. R. China

Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China

E-mail Address: weizhouchao@163.com

E-mail Address: weizc@cug.edu.cn

Corresponding author.

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IRENE MOROZ

https://orcid.org/0000-0003-1503-939X

Mathematical Institute, Oxford University, Oxford, OX2 6GG, UK

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, and

ABDULWASEA ALKHAZZAN

https://orcid.org/0000-0002-6504-8705

School of Mathematics and Statistic, Northwestern Polytechnical University, Shannxi, 710072 Xi’an, P. R. China

E-mail Address: alkhazan84@yahoo.com

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https://doi.org/10.1142/S0218348X23400856Cited by:5 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems IV
Guest Editors: Yeliz Karaca, Dumitru Baleanu, Majaz Moonis, Yu-Dong Zhang and Osvaldo Gervasi

Abstract

This paper investigates the necessary conditions relating to the existence and uniqueness of solution to impulsive system fractional differential equation with a nonlinear p-Laplacian operator. Our problem is based on two kinds of fractional order derivatives. That is, Atangana–Baleanu–Caputo (ABC) fractional derivative and the Caputo–Fabrizio derivative. To achieve our main aims, we will first convert the proposed impulse system into an integral equation form. Next, we prove the existence and uniqueness of solutions with the help of Leray–Schauder’s theory and the Banach contraction principle. We analyze the operator for continuity, boundedness, and equicontinuity. Further, we investigate the stability solution to the proposed impulsive system by using stability techniques. In the last part, we demonstrate the results via an illustrative example for the application of the results.

Keywords:

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Vol. 31, No. 10

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History

Received 15 March 2022

Accepted 5 December 2022

Published: September 27, 2023

Information

This is an Open Access article in the “Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part IV”, edited by Yeliz Karaca https://orcid.org/0000-0001-8725-6719 (University of Massachusetts Chan Medical School, USA), Dumitru Baleanu https://orcid.org/0000-0002-0286-7244 (Cankaya University, Turkey & Institute of Space Sciences, Romania), Majaz Moonis https://orcid.org/0000-0002-9747-0003 (University of Massachusetts Chan Medical School, USA), Yu-Dong Zhang https://orcid.org/0000-0002-4870-1493 (University of Leicester, Leicester, UK) & Osvaldo Gervasi https://orcid.org/0000-0003-4327-520X (Perugia University, Perugia, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND) License which permits use, distribution and reproduction, provided that the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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EXISTENCE AND STABILITY OF SOLUTION IN BANACH SPACE FOR AN IMPULSIVE SYSTEM INVOLVING ATANGANA–BALEANU AND CAPUTO–FABRIZIO DERIVATIVES

Abstract

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