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Volume 14
Issue 9
10.3390/axioms14090685
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Coupled System of (k,ψ)-Hilfer and (k,ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions

by
Furkan Erkan
1,
Nuket Aykut Hamal
1,
Sotiris K. Ntouyas
2,
Jessada Tariboon
3 and
Phollakrit Wongsantisuk
4,*
1
Department of Mathematics, Ege University, Bornova 35100, Izmir, Türkiye
2
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
3
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
4
Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(9), 685; https://doi.org/10.3390/axioms14090685 (registering DOI)
Submission received: 13 July 2025 / Revised: 1 August 2025 / Accepted: 4 September 2025 / Published: 7 September 2025
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)
Versions Notes

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of (k,ψ)-Hilfer and (k,ψ)-Caputo sequential fractional differential equations with non-separated boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while two existence results are proved by using Leray–Schauder nonlinear alternative and Krasnosel’skiĭ’s fixed point theorem. The obtained results are illustrated by numerical examples.
Keywords: coupled sytems; (k,ψ)-Hilfer fractional derivative; (k,ψ)-Caputo fractional derivative; boundary value problems; existence and uniqueness coupled sytems; (k,ψ)-Hilfer fractional derivative; (k,ψ)-Caputo fractional derivative; boundary value problems; existence and uniqueness

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MDPI and ACS Style

Erkan, F.; Hamal, N.A.; Ntouyas, S.K.; Tariboon, J.; Wongsantisuk, P. Coupled System of (k,ψ)-Hilfer and (k,ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions. Axioms 2025, 14, 685. https://doi.org/10.3390/axioms14090685

AMA Style

Erkan F, Hamal NA, Ntouyas SK, Tariboon J, Wongsantisuk P. Coupled System of (k,ψ)-Hilfer and (k,ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions. Axioms. 2025; 14(9):685. https://doi.org/10.3390/axioms14090685

Chicago/Turabian Style

Erkan, Furkan, Nuket Aykut Hamal, Sotiris K. Ntouyas, Jessada Tariboon, and Phollakrit Wongsantisuk. 2025. "Coupled System of (k,ψ)-Hilfer and (k,ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions" Axioms 14, no. 9: 685. https://doi.org/10.3390/axioms14090685

APA Style

Erkan, F., Hamal, N. A., Ntouyas, S. K., Tariboon, J., & Wongsantisuk, P. (2025). Coupled System of (k,ψ)-Hilfer and (k,ψ)-Caputo Sequential Fractional Differential Equations with Non-Separated Boundary Conditions. Axioms, 14(9), 685. https://doi.org/10.3390/axioms14090685

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