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Research Article | Open Access

Mixed Erdélyi-Kober and Caputo fractional differential equations with nonlocal non-separated boundary conditions

Ayub Samadi1, Chaiyod Kamthorncharoen2, Sotiris K. Ntouyas3, Jessada Tariboon2( )
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, 5315836511, Iran
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
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
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Abstract

In this paper, we investigate a sequential fractional boundary value problem that contains a combination of Erdélyi-Kober and Caputo fractional derivative operators subject to nonlocal, non-separated boundary conditions. We establish the uniqueness of the solution by using Banach's fixed point theorem, while via Krasnosel'skiĭ's fixed-point theorem and Leray-Schauder's nonlinear alternative, we prove the existence results. The obtained results are illustrated by constructed numerical examples.

Keywords

Erdélyi-Kober fractional derivativeCaputo fractional derivativeexistence and uniquenessfixed point theoremsnonlocal boundary conditions
CLC number: 26A33, 34A08, 34B15

References

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 32904-32920
DOI: 10.3934/math.20241574

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Samadi A, Kamthorncharoen C, Ntouyas SK, et al. Mixed Erdélyi-Kober and Caputo fractional differential equations with nonlocal non-separated boundary conditions. AIMS Mathematics, 2024, 9(11): 32904-32920. https://doi.org/10.3934/math.20241574

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Received: 06 September 2024
Revised: 11 November 2024
Accepted: 13 November 2024
Published: 20 November 2024
©2024 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)