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Research Article | Open Access

On a nonlinear coupled Caputo-type fractional differential system with coupled closed boundary conditions

Ahmed Alsaedi1, Manal Alnahdi1, Bashir Ahmad1( ), Sotiris K. Ntouyas1,2
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, University of Ioannina, 45110, Ioannina, Greece
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Abstract

We introduce a novel notion of coupled closed boundary conditions and investigate a nonlinear system of Caputo fractional differential equations equipped with these conditions. The existence result for the given problem is proved via the Leray-Schauder alternative, while the uniqueness of its solutions is accomplished by applying the Banach fixed point theorem. Examples are constructed for the illustration of the main results. Some special cases arising from the present study are discussed.

Keywords

Caputo fractional derivativesystemcoupled closed boundary conditionsexistencefixed point theorems
CLC number: 34A08, 34B15

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 17981-17995
DOI: 10.3934/math.2023914

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Cite this article:
Alsaedi A, Alnahdi M, Ahmad B, et al. On a nonlinear coupled Caputo-type fractional differential system with coupled closed boundary conditions. AIMS Mathematics, 2023, 8(8): 17981-17995. https://doi.org/10.3934/math.2023914

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Received: 10 February 2023
Revised: 03 May 2023
Accepted: 09 May 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)