Coupled systems of $ \psi $-Hilfer generalized proportional fractional nonlocal mixed boundary value problems

Sunisa Theswan; Sotiris K. Ntouyas; Jessada Tariboon; Sunisa Theswan; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.20231122

AIMS Mathematics

2023, Volume 8, Issue 9: 22009-22036. doi: 10.3934/math.20231122

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Research article

Coupled systems of $ \psi $-Hilfer generalized proportional fractional nonlocal mixed boundary value problems

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, Ioannina 45110, Greece

Received: 17 April 2023 Revised: 25 June 2023 Accepted: 30 June 2023 Published: 11 July 2023
MSC : 26A33, 34A08, 34B10

In this paper, we investigate a coupled system of Hilfer-type nonlinear proportional fractional differential equations supplemented with mixed multi-point and integro-multi-point boundary conditions. We used standard methods from functional analysis and especially fixed point theory. Two existence results are established using the Leray-Schauder's alternative and the Krasnosel'skii's fixed point theorem, while the existence of a unique solution is achieved via the Banach's contraction mapping principle. Finally, numerical examples are constructed to illustrate the main theoretical results. Our results are novel, wider in scope, produce a variety of new results as special cases and contribute to the existing literature on nonlocal systems of nonlinear $ \psi $-Hilfer generalized fractional proportional differential equations.
- coupled system,
- Hilfer fractional proportional derivative,
- nonlocal boundary conditions,
- multi-point boundary conditions,
- integral boundary conditions,
- fixed point theorems
Citation: Sunisa Theswan, Sotiris K. Ntouyas, Jessada Tariboon. Coupled systems of $ \psi $-Hilfer generalized proportional fractional nonlocal mixed boundary value problems[J]. AIMS Mathematics, 2023, 8(9): 22009-22036. doi: 10.3934/math.20231122

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Abstract

In this paper, we investigate a coupled system of Hilfer-type nonlinear proportional fractional differential equations supplemented with mixed multi-point and integro-multi-point boundary conditions. We used standard methods from functional analysis and especially fixed point theory. Two existence results are established using the Leray-Schauder's alternative and the Krasnosel'skii's fixed point theorem, while the existence of a unique solution is achieved via the Banach's contraction mapping principle. Finally, numerical examples are constructed to illustrate the main theoretical results. Our results are novel, wider in scope, produce a variety of new results as special cases and contribute to the existing literature on nonlocal systems of nonlinear $ \psi $-Hilfer generalized fractional proportional differential equations.

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