Existence results for a coupled system of $ (k, \varphi) $-Hilfer fractional differential equations with nonlocal integro-multi-point boundary conditions

Nattapong Kamsrisuk; Sotiris K. Ntouyas; Bashir Ahmad; Ayub Samadi; Jessada Tariboon; Nattapong Kamsrisuk; Sotiris K. Ntouyas; Bashir Ahmad; Ayub Samadi; Jessada Tariboon

doi:10.3934/math.2023203

AIMS Mathematics

2023, Volume 8, Issue 2: 4079-4097. doi: 10.3934/math.2023203

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Existence results for a coupled system of $ (k, \varphi) $-Hilfer fractional differential equations with nonlocal integro-multi-point boundary conditions

1.
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
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
4.
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran

Received: 30 August 2022 Revised: 04 November 2022 Accepted: 17 November 2022 Published: 01 December 2022
MSC : 34A08, 34B10

In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of $ (k, \varphi) $-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $'s fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters $ \beta_1, $ $ \beta_2, $ and the function $ \varphi $ involved in the problem at hand.
- $ (k, \varphi) $-Hilfer fractional derivative,
- Riemann-Liouville fractional derivative,
- Caputo fractional derivative,
- existence,
- uniqueness,
- fixed point theorems
Citation: Nattapong Kamsrisuk, Sotiris K. Ntouyas, Bashir Ahmad, Ayub Samadi, Jessada Tariboon. Existence results for a coupled system of $ (k, \varphi) $-Hilfer fractional differential equations with nonlocal integro-multi-point boundary conditions[J]. AIMS Mathematics, 2023, 8(2): 4079-4097. doi: 10.3934/math.2023203

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Abstract

In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of $ (k, \varphi) $-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $'s fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters $ \beta_1, $ $ \beta_2, $ and the function $ \varphi $ involved in the problem at hand.

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