Analytical solution of the systems of nonlinear fractional partial differential equations using conformable Laplace transform iterative method

Nisar Gul; Saima Noor; Abdulkafi Mohammed Saeed; Musaad S. Aldhabani; Roman Ullah; Nisar Gul; Saima Noor; Abdulkafi Mohammed Saeed; Musaad S. Aldhabani; Roman Ullah

doi:10.3934/math.2025091

AIMS Mathematics

2025, Volume 10, Issue 2: 1945-1966. doi: 10.3934/math.2025091

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Analytical solution of the systems of nonlinear fractional partial differential equations using conformable Laplace transform iterative method

1.
School of Mathematics and Statistics, Central South University, Changsha 410083, China
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, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; abdulkafi.ahmed@qu.edu.sa
5.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia; maldhabani@ut.edu.sa
6.
Department of General Studies, Higher Colleges of Technology, Dubai Women Campus, UAE

Received: 14 November 2024 Revised: 21 December 2024 Accepted: 21 January 2025 Published: 07 February 2025
MSC : 35J05, 35J10

In this study, we presented the conformable Laplace transform iterative method to find the approximate solution of the systems of nonlinear temporal-fractional differential equations in the sense of the conformable derivative. The advantage of the suggested approach was to compute the solution without discretization and restrictive assumptions. Three distinct examples were provided to show the applicability and efficacy of the proposed approach. To examine the exact and approximate solutions, we utilized the 2D and 3D graphics. Furthermore, the outcomes produced in this study were consistent with the exact solutions; hence, this strategy efficiently and effectively determined exact and approximate solutions to nonlinear temporal-fractional differential equations.
- temporal-fractional differential equations,
- conformable Laplace transform,
- iterative method,
- conformable derivative,
- numerical experiments
Citation: Nisar Gul, Saima Noor, Abdulkafi Mohammed Saeed, Musaad S. Aldhabani, Roman Ullah. Analytical solution of the systems of nonlinear fractional partial differential equations using conformable Laplace transform iterative method[J]. AIMS Mathematics, 2025, 10(2): 1945-1966. doi: 10.3934/math.2025091

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Abstract

In this study, we presented the conformable Laplace transform iterative method to find the approximate solution of the systems of nonlinear temporal-fractional differential equations in the sense of the conformable derivative. The advantage of the suggested approach was to compute the solution without discretization and restrictive assumptions. Three distinct examples were provided to show the applicability and efficacy of the proposed approach. To examine the exact and approximate solutions, we utilized the 2D and 3D graphics. Furthermore, the outcomes produced in this study were consistent with the exact solutions; hence, this strategy efficiently and effectively determined exact and approximate solutions to nonlinear temporal-fractional differential equations.

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