Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions

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

doi:10.3934/math.2024633

AIMS Mathematics

2024, Volume 9, Issue 5: 12982-13005. doi: 10.3934/math.2024633

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Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions

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

Received: 27 February 2024 Revised: 27 March 2024 Accepted: 29 March 2024 Published: 07 April 2024
MSC : 26A33, 34A08, 34B15

In this paper, we studied the existence of solutions for a coupled system of nonlinear sequential proportional $ \psi $-Hilfer fractional differential equations with multi-point boundary conditions. By using a Burton's version of the Krasnosel'ski$\breve{{\rm{i}}}$'s fixed-point theorem we established sufficient conditions for the existence result. An example illustrating our main result was also provided.
- coupled system,
- Hilfer fractional proportional derivative,
- multi-point boundary conditions,
- fixed-point theorem
Citation: Ayub Samadi, Sotiris K. Ntouyas, Jessada Tariboon. Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions[J]. AIMS Mathematics, 2024, 9(5): 12982-13005. doi: 10.3934/math.2024633

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Abstract

In this paper, we studied the existence of solutions for a coupled system of nonlinear sequential proportional $ \psi $-Hilfer fractional differential equations with multi-point boundary conditions. By using a Burton's version of the Krasnosel'ski$\breve{{\rm{i}}}$'s fixed-point theorem we established sufficient conditions for the existence result. An example illustrating our main result was also provided.

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