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

Mesmouli, Mouataz Billah; Iambor, Loredana Florentina; Abdel Menaem, Amir; Hassan, Taher S.

doi:10.3390/math12091399

Open AccessArticle

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

by

Mouataz Billah Mesmouli

^1,*

,

Loredana Florentina Iambor

^2,*

,

Amir Abdel Menaem

³

and

Taher S. Hassan

^1,4,5

¹

Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

²

Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

³

Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia

⁴

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

⁵

Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy

^*

Authors to whom correspondence should be addressed.

Mathematics 2024, 12(9), 1399; https://doi.org/10.3390/math12091399

Submission received: 15 March 2024 / Revised: 20 April 2024 / Accepted: 30 April 2024 / Published: 3 May 2024

(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition)

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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

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MDPI and ACS Style

Mesmouli, M.B.; Iambor, L.F.; Abdel Menaem, A.; Hassan, T.S. Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System. Mathematics 2024, 12, 1399. https://doi.org/10.3390/math12091399

AMA Style

Mesmouli MB, Iambor LF, Abdel Menaem A, Hassan TS. Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System. Mathematics. 2024; 12(9):1399. https://doi.org/10.3390/math12091399

Chicago/Turabian Style

Mesmouli, Mouataz Billah, Loredana Florentina Iambor, Amir Abdel Menaem, and Taher S. Hassan. 2024. "Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System" Mathematics 12, no. 9: 1399. https://doi.org/10.3390/math12091399

APA Style

Mesmouli, M. B., Iambor, L. F., Abdel Menaem, A., & Hassan, T. S. (2024). Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System. Mathematics, 12(9), 1399. https://doi.org/10.3390/math12091399

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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