Innovative approaches of a time-fractional system of Boussinesq equations within a Mohand transform

Meshari Alesemi; Meshari Alesemi

doi:10.3934/math.20241419

AIMS Mathematics

2024, Volume 9, Issue 10: 29269-29295. doi: 10.3934/math.20241419

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Research article

Innovative approaches of a time-fractional system of Boussinesq equations within a Mohand transform

Meshari Alesemi ^,

Department of Mathematics, College of Science, University of Bisha, P.O. Box 511, Bisha 61922, Saudi Arabia

Received: 25 August 2024 Revised: 21 September 2024 Accepted: 08 October 2024 Published: 16 October 2024
MSC : 34G20, 35A20, 35A22, 35R11

This paper investigated the application of analytical methods, specifically the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM), to solve the fractional Boussinesq equation. Utilizing the Caputo operator to manage fractional derivatives, these semi-analytical approaches provide accurate solutions to complex fractional differential equations. Through convergence analysis and error estimation, the study validated the efficacy of these methods by comparing numerical solutions to known exact solutions. Graphical and tabular representations illustrated the accuracy of the proposed methods, highlighting their performance for varying fractional orders. The findings demonstrated that both MTIM and MRPSM offer reliable, efficient solutions, making them valuable tools for addressing fractional differential systems in fields such as applied mathematics, engineering, and physics.
- Boussinesq equation,
- Mohand transform iterative method,
- Mohand residual power series method,
- fractional-order differential equation,
- Caputo operator
Citation: Meshari Alesemi. Innovative approaches of a time-fractional system of Boussinesq equations within a Mohand transform[J]. AIMS Mathematics, 2024, 9(10): 29269-29295. doi: 10.3934/math.20241419

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Abstract

This paper investigated the application of analytical methods, specifically the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM), to solve the fractional Boussinesq equation. Utilizing the Caputo operator to manage fractional derivatives, these semi-analytical approaches provide accurate solutions to complex fractional differential equations. Through convergence analysis and error estimation, the study validated the efficacy of these methods by comparing numerical solutions to known exact solutions. Graphical and tabular representations illustrated the accuracy of the proposed methods, highlighting their performance for varying fractional orders. The findings demonstrated that both MTIM and MRPSM offer reliable, efficient solutions, making them valuable tools for addressing fractional differential systems in fields such as applied mathematics, engineering, and physics.

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