Analyzing fractional PDE system with the Caputo operator and Mohand transform techniques

Azzh Saad Alshehry; Humaira Yasmin; Ali M. Mahnashi; Azzh Saad Alshehry; Humaira Yasmin; Ali M. Mahnashi

doi:10.3934/math.20241544

AIMS Mathematics

2024, Volume 9, Issue 11: 32157-32181. doi: 10.3934/math.20241544

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Analyzing fractional PDE system with the Caputo operator and Mohand transform techniques

1.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia

Received: 03 September 2024 Revised: 21 October 2024 Accepted: 31 October 2024 Published: 13 November 2024
MSC : 34G20, 35A20, 35A22, 35R11

In this paper, we explore advanced methods for solving partial differential equations (PDEs) and systems of PDEs, particularly those involving fractional-order derivatives. We apply the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM) to address the complexities associated with fractional-order differential equations. Through several examples, we demonstrate the effectiveness and accuracy of MTIM and MRPSM in solving fractional PDEs. The results indicate that these methods simplify the solution process and enhance the solutions' precision. Our findings suggest that these approaches can be valuable tools for researchers dealing with complex PDE systems in various scientific and engineering fields.
- PDE and system of PDEs,
- MTIM,
- MRPSM,
- fractional order differential equation,
- Caputo operator
Citation: Azzh Saad Alshehry, Humaira Yasmin, Ali M. Mahnashi. Analyzing fractional PDE system with the Caputo operator and Mohand transform techniques[J]. AIMS Mathematics, 2024, 9(11): 32157-32181. doi: 10.3934/math.20241544

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Abstract

In this paper, we explore advanced methods for solving partial differential equations (PDEs) and systems of PDEs, particularly those involving fractional-order derivatives. We apply the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM) to address the complexities associated with fractional-order differential equations. Through several examples, we demonstrate the effectiveness and accuracy of MTIM and MRPSM in solving fractional PDEs. The results indicate that these methods simplify the solution process and enhance the solutions' precision. Our findings suggest that these approaches can be valuable tools for researchers dealing with complex PDE systems in various scientific and engineering fields.

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