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

Ahmed Alsaedi; Manal Alnahdi; Bashir Ahmad; Sotiris K. Ntouyas; Ahmed Alsaedi; Manal Alnahdi; Bashir Ahmad; Sotiris K. Ntouyas

doi:10.3934/math.2023914

AIMS Mathematics

2023, Volume 8, Issue 8: 17981-17995. doi: 10.3934/math.2023914

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

1.
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
2.
Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece

Received: 10 February 2023 Revised: 03 May 2023 Accepted: 09 May 2023 Published: 24 May 2023
MSC : 34A08, 34B15

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.
- Caputo fractional derivative,
- system,
- coupled closed boundary conditions,
- existence,
- fixed point theorems
Citation: Ahmed Alsaedi, Manal Alnahdi, Bashir Ahmad, Sotiris K. Ntouyas. On a nonlinear coupled Caputo-type fractional differential system with coupled closed boundary conditions[J]. AIMS Mathematics, 2023, 8(8): 17981-17995. doi: 10.3934/math.2023914

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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.

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