Unification of Adomian decomposition method and ZZ transformation for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems

Yousef Jawarneh; Humaira Yasmin; Abdul Hamid Ganie; M. Mossa Al-Sawalha; Amjid Ali; Yousef Jawarneh; Humaira Yasmin; Abdul Hamid Ganie; M. Mossa Al-Sawalha; Amjid Ali

doi:10.3934/math.2024021

AIMS Mathematics

2024, Volume 9, Issue 1: 371-390. doi: 10.3934/math.2024021

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Unification of Adomian decomposition method and ZZ transformation for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Basic Sciences, General Administration of the Preparatory Year, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
3.
Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
4.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Khyber Pakhtunkhwa, Pakistan
5.
Department of Information Science, Faculty of Science and Engineering, Saga University, Japan

Received: 31 August 2023 Revised: 11 November 2023 Accepted: 14 November 2023 Published: 29 November 2023
MSC : 33B15, 34A34, 35A20, 35A22, 44A10

This paper presents a novel approach for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems by using the unification of the Adomian decomposition method and ZZ transformation. The suggested method combines the Aboodh transform and the Adomian decomposition method, both of which are trustworthy and efficient mathematical tools for solving fractional differential equations (FDEs). This method's theoretical analysis is addressed for nonlinear FDE systems. To find exact solutions to the equations, the method is applied to fractional Kersten-Krasil'shchik linked KdV-mKdV systems. The results show that the suggested method is efficient and practical for solving fractional Kersten-Krasil'shchik linked KdV-mKdV systems and that it may be applied to other nonlinear FDEs. The suggested method has the potential to provide new insights into the behavior of nonlinear waves in fluid and plasma environments, as well as the development of new mathematical tools for modeling and studying complicated wave phenomena.
- Korteweg-de Vries nonlinear system,
- Adomian decomposition method,
- ZZ transform,
- Atangana-Baleanu operator
Citation: Yousef Jawarneh, Humaira Yasmin, Abdul Hamid Ganie, M. Mossa Al-Sawalha, Amjid Ali. Unification of Adomian decomposition method and ZZ transformation for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems[J]. AIMS Mathematics, 2024, 9(1): 371-390. doi: 10.3934/math.2024021

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Abstract

This paper presents a novel approach for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems by using the unification of the Adomian decomposition method and ZZ transformation. The suggested method combines the Aboodh transform and the Adomian decomposition method, both of which are trustworthy and efficient mathematical tools for solving fractional differential equations (FDEs). This method's theoretical analysis is addressed for nonlinear FDE systems. To find exact solutions to the equations, the method is applied to fractional Kersten-Krasil'shchik linked KdV-mKdV systems. The results show that the suggested method is efficient and practical for solving fractional Kersten-Krasil'shchik linked KdV-mKdV systems and that it may be applied to other nonlinear FDEs. The suggested method has the potential to provide new insights into the behavior of nonlinear waves in fluid and plasma environments, as well as the development of new mathematical tools for modeling and studying complicated wave phenomena.

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