Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part IIOpen Access

EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL $q$ $q$ -INTEGRO-DIFFERENCE EQUATIONS WITH $q$ $q$ -INTEGRAL-COUPLED BOUNDARY CONDITIONS

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: aalsaedi@hotmail.com

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HANA AL-HUTAMI

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: hanno.1407@hotmail.com

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BASHIR AHMAD

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: bashirahmad_qau@yahoo.com

Corresponding author.

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, and

RAVI P. AGARWAL

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Department of Mathematics, Texas A & M University, Kingsville, Texas 78363-8202, USA

E-mail Address: Ravi.Agarwal@tamuk.edu

Corresponding author.

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https://doi.org/10.1142/S0218348X22400424Cited by:21 (Source: Crossref)

Abstract

In this paper, we introduce and investigate a new class of coupled fractional $q$ $q$ -integro-difference equations involving Riemann–Liouville fractional $q$ $q$ -derivatives and $q$ $q$ -integrals of different orders, equipped with $q$ $q$ -integral-coupled boundary conditions. The given problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed-points coincide with solutions of the problem at hand. The existence and uniqueness results for the given problem are, respectively, derived by applying Leray–Schauder nonlinear alternative and Banach contraction mapping principle. Illustrative examples for the obtained results are constructed. This paper concludes with some interesting observations and special cases dealing with uncoupled boundary conditions, and non-integral and integral types nonlinearities.

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Vol. 30, No. 01

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History

Received 10 July 2021

Accepted 30 August 2021

Published: October 9, 2021

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part II”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Khan Muhammad (Sejong University, South Korea), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL qq<math altimg="eq-00001.gif" display="inline"><mi>q</mi></math>-INTEGRO-DIFFERENCE EQUATIONS WITH qq<math altimg="eq-00002.gif" display="inline"><mi>q</mi></math>-INTEGRAL-COUPLED BOUNDARY CONDITIONS

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EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL $q$ $q$ -INTEGRO-DIFFERENCE EQUATIONS WITH $q$ $q$ -INTEGRAL-COUPLED BOUNDARY CONDITIONS