Existence Results and Finite-Time Stability of a Fractional ( p, q )-Integro-Difference System

Mouataz Billah Mesmouli (), Loredana Florentina Iambor (), Amir Abdel Menaem and Taher S. Hassan
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Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Loredana Florentina Iambor: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Amir Abdel Menaem: Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Taher S. Hassan: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2024, vol. 12, issue 9, 1-12

Abstract: In this article, we mainly generalize the results in the literature for a fractional q -difference equation. Our study considers a more comprehensive type of fractional p , q -difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii’s fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work.

Keywords: fractional-order derivative; ( p , q )-difference calculus; stability; fixed-point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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