Coupled system of $ (k, \psi) $-Caputo fractional boundary value problems involving multi-point fractional closed boundary conditions

Furkan Erkan; Nuket Aykut Hamal; Sotiris K. Ntouyas; Bashir Ahmad; Furkan Erkan; Nuket Aykut Hamal; Sotiris K. Ntouyas; Bashir Ahmad

doi:10.3934/math.2026110

AIMS Mathematics

2026, Volume 11, Issue 1: 2722-2746. doi: 10.3934/math.2026110

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Coupled system of $ (k, \psi) $-Caputo fractional boundary value problems involving multi-point fractional closed boundary conditions

1.
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Türkiye
2.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
3.
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

Received: 05 January 2026 Revised: 22 January 2026 Accepted: 26 January 2026 Published: 28 January 2026
MSC : 34A08, 34B10, 34B15

This work is devoted to the analysis of a coupled system of $ (k, \psi) $-Caputo fractional differential equations equipped with fractional closed boundary conditions. We establish the uniqueness of solutions by applying Banach's contraction principle, and existence is obtained through the Leray–Schauder alternative. Illustrative examples are included to demonstrate the effectiveness and practical relevance of the theoretical results.
- coupled systems,
- $ (k, \psi) $-Caputo fractional derivative,
- existence and uniqueness,
- fixed point theory,
- Leray–Schauder alternative
Citation: Furkan Erkan, Nuket Aykut Hamal, Sotiris K. Ntouyas, Bashir Ahmad. Coupled system of $ (k, \psi) $-Caputo fractional boundary value problems involving multi-point fractional closed boundary conditions[J]. AIMS Mathematics, 2026, 11(1): 2722-2746. doi: 10.3934/math.2026110

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Abstract

This work is devoted to the analysis of a coupled system of $ (k, \psi) $-Caputo fractional differential equations equipped with fractional closed boundary conditions. We establish the uniqueness of solutions by applying Banach's contraction principle, and existence is obtained through the Leray–Schauder alternative. Illustrative examples are included to demonstrate the effectiveness and practical relevance of the theoretical results.

References

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