Analysis on existence of system of coupled multifractional nonlinear hybrid differential equations with coupled boundary conditions

M. Latha Maheswari; K. S. Keerthana Shri; Mohammad Sajid; M. Latha Maheswari; K. S. Keerthana Shri; Mohammad Sajid

doi:10.3934/math.2024666

AIMS Mathematics

2024, Volume 9, Issue 6: 13642-13658. doi: 10.3934/math.2024666

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Analysis on existence of system of coupled multifractional nonlinear hybrid differential equations with coupled boundary conditions

1.
Department of Mathematics, PSG College of Arts & Science, Coimbatore, Tamil Nadu, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia

Received: 22 January 2024 Revised: 11 April 2024 Accepted: 11 April 2024 Published: 12 April 2024
MSC : 26A33, 34A12, 34A38, 47H10

This article dealt with a class of coupled hybrid fractional differential system. It consisted of a mixed type of Caputo and Hilfer fractional derivatives with respect to two different kernel functions, $ \psi_{_1} $ and $ \psi_{_2} $, respectively, in addition to coupled boundary conditions. The existence of the solution of the system was investigated using the Dhage fixed point theorem. Finally, an illustration was presented to validate our findings.
- $ \psi $-Hilfer and $ \psi $-Caputo fractional derivatives,
- hybrid fractional differential equations,
- fixed point theory,
- existence
Citation: M. Latha Maheswari, K. S. Keerthana Shri, Mohammad Sajid. Analysis on existence of system of coupled multifractional nonlinear hybrid differential equations with coupled boundary conditions[J]. AIMS Mathematics, 2024, 9(6): 13642-13658. doi: 10.3934/math.2024666

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Abstract

This article dealt with a class of coupled hybrid fractional differential system. It consisted of a mixed type of Caputo and Hilfer fractional derivatives with respect to two different kernel functions, $ \psi_{_1} $ and $ \psi_{_2} $, respectively, in addition to coupled boundary conditions. The existence of the solution of the system was investigated using the Dhage fixed point theorem. Finally, an illustration was presented to validate our findings.

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