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

Ayub Samadi; Chaiyod Kamthorncharoen; Sotiris K. Ntouyas; Jessada Tariboon; Ayub Samadi; Chaiyod Kamthorncharoen; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.20241574

AIMS Mathematics

2024, Volume 9, Issue 11: 32904-32920. doi: 10.3934/math.20241574

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Research article

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

1.
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, 5315836511, Iran
2.
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
3.
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Received: 06 September 2024 Revised: 11 November 2024 Accepted: 13 November 2024 Published: 20 November 2024
MSC : 26A33, 34A08, 34B15

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.
- Erdélyi-Kober fractional derivative,
- Caputo fractional derivative,
- existence and uniqueness,
- fixed point theorems,
- nonlocal boundary conditions
Citation: Ayub Samadi, Chaiyod Kamthorncharoen, Sotiris K. Ntouyas, Jessada Tariboon. Mixed Erdélyi-Kober and Caputo fractional differential equations with nonlocal non-separated boundary conditions[J]. AIMS Mathematics, 2024, 9(11): 32904-32920. doi: 10.3934/math.20241574

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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.

References

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