Numerical investigation of systems of fractional partial differential equations by new transform iterative technique

Mariam Sultana; Muhammad Waqar; Ali Hasan Ali; Alina Alb Lupaş; F. Ghanim; Zaid Ameen Abduljabbar; Mariam Sultana; Muhammad Waqar; Ali Hasan Ali; Alina Alb Lupaş; F. Ghanim; Zaid Ameen Abduljabbar

doi:10.3934/math.20241296

AIMS Mathematics

2024, Volume 9, Issue 10: 26649-26670. doi: 10.3934/math.20241296

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Research article

Numerical investigation of systems of fractional partial differential equations by new transform iterative technique

1.
Department of Mathematical Sciences, Federal Urdu University of Arts, Sciences and Technology, Gulshan-e-Iqbal Campus, University Road, Karachi-75300, Karachi, Pakistan
2.
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
3.
Department of Business Management, Al-imam University College, 34011 Balad, Iraq
4.
Technical Engineering College, Al-Ayen University, Dhi Qar 64001, Iraq
5.
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 14 Oradea, Romania
6.
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates
7.
Department of Computer Science, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq

Received: 09 July 2024 Revised: 23 August 2024 Accepted: 27 August 2024 Published: 13 September 2024
MSC : 65R10, 34A08, 35R11

This research introduced a new method, the Aboodh Tamimi Ansari transform method ($ (AT)^2 $ method), for solving systems of linear and nonlinear fractional partial differential equations. The method combined the Aboodh transform method and the Tamimi Ansari method, allowing for the simultaneous solution of linear and nonlinear terms without restrictions. The Caputo sense was considered for fractional derivatives. The effectiveness of the proposed method was demonstrated through numerical solutions, graphical representations, and tabular data, showing strong agreement with exact solutions. The approach was deemed precise, easy to apply, and could be extended to address further challenges in fractional-order problems. Computational tasks were carried out using Mathematica 13.
- fractional calculus,
- Caputo derivative,
- linear and nonlinear,
- system of partial differential equations,
- Aboodh transform,
- Tamimi Ansari method
Citation: Mariam Sultana, Muhammad Waqar, Ali Hasan Ali, Alina Alb Lupaş, F. Ghanim, Zaid Ameen Abduljabbar. Numerical investigation of systems of fractional partial differential equations by new transform iterative technique[J]. AIMS Mathematics, 2024, 9(10): 26649-26670. doi: 10.3934/math.20241296

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Abstract

This research introduced a new method, the Aboodh Tamimi Ansari transform method ($ (AT)^2 $ method), for solving systems of linear and nonlinear fractional partial differential equations. The method combined the Aboodh transform method and the Tamimi Ansari method, allowing for the simultaneous solution of linear and nonlinear terms without restrictions. The Caputo sense was considered for fractional derivatives. The effectiveness of the proposed method was demonstrated through numerical solutions, graphical representations, and tabular data, showing strong agreement with exact solutions. The approach was deemed precise, easy to apply, and could be extended to address further challenges in fractional-order problems. Computational tasks were carried out using Mathematica 13.

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