Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions

Salma Noor; Aman Ullah; Anwar Ali; Saud Fahad Aldosary; Salma Noor; Aman Ullah; Anwar Ali; Saud Fahad Aldosary

doi:10.3934/math.2024785

AIMS Mathematics

2024, Volume 9, Issue 6: 16234-16249. doi: 10.3934/math.2024785

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Research article

Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions

1.
Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

Received: 30 January 2024 Revised: 06 April 2024 Accepted: 17 April 2024 Published: 08 May 2024
MSC : 26A33, 34A08, 34K38

In this paper, we investigated $ n $-dimensional fractional hybrid differential equations (FHDEs) with nonlinear boundary conditions in a nonlinear coupled system. For this purpose, we used Dhage's fixed point theory, and applied the Krasnoselskii-type coupled fixed point theorem to construct existence conditions of the solution of the FHDEs. To illustrated this idea, suitable examples are presented in $ 3 $-dimensional space at the end of the paper.
- $ n $-dimensional nonlinear coupled system,
- fractional hybrid differential equations,
- Dhage's fixed point theory
Citation: Salma Noor, Aman Ullah, Anwar Ali, Saud Fahad Aldosary. Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions[J]. AIMS Mathematics, 2024, 9(6): 16234-16249. doi: 10.3934/math.2024785

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Abstract

In this paper, we investigated $ n $-dimensional fractional hybrid differential equations (FHDEs) with nonlinear boundary conditions in a nonlinear coupled system. For this purpose, we used Dhage's fixed point theory, and applied the Krasnoselskii-type coupled fixed point theorem to construct existence conditions of the solution of the FHDEs. To illustrated this idea, suitable examples are presented in $ 3 $-dimensional space at the end of the paper.

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