Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives

M. Mossa Al-Sawalha; Rasool Shah; Adnan Khan; Osama Y. Ababneh; Thongchai Botmart; M. Mossa Al-Sawalha; Rasool Shah; Adnan Khan; Osama Y. Ababneh; Thongchai Botmart

doi:10.3934/math.20221010

AIMS Mathematics

2022, Volume 7, Issue 10: 18334-18359. doi: 10.3934/math.20221010

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Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives

1.
Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
3.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 02 July 2022 Revised: 12 July 2022 Accepted: 25 July 2022 Published: 15 August 2022
MSC : 34A34, 35A20, 35A22, 44A10, 33B15

The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Korteweg-de Vries system is obtained in this study by employing a natural decomposition method in association with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The Korteweg-de Vries equation is considered a classical super-extension in this system. This nonlinear model scheme is commonly used to describe waves in traffic flow, electromagnetism, electrodynamics, elastic media, multi-component plasmas, shallow water waves and other phenomena. The acquired results are compared to exact solutions to demonstrate the suggested method's effectiveness and reliability. Graphs and tables are used to display the numerical results. The results show that the natural decomposition technique is a very user-friendly and reliable method for dealing with fractional order nonlinear problems.
- Natural transform,
- Adomian decomposition method,
- Caputo-Fabrizio derivative,
- Atangana-Baleanu-Caputo operator,
- Korteweg-de Vries nonlinear system
Citation: M. Mossa Al-Sawalha, Rasool Shah, Adnan Khan, Osama Y. Ababneh, Thongchai Botmart. Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives[J]. AIMS Mathematics, 2022, 7(10): 18334-18359. doi: 10.3934/math.20221010

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Abstract

The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Korteweg-de Vries system is obtained in this study by employing a natural decomposition method in association with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The Korteweg-de Vries equation is considered a classical super-extension in this system. This nonlinear model scheme is commonly used to describe waves in traffic flow, electromagnetism, electrodynamics, elastic media, multi-component plasmas, shallow water waves and other phenomena. The acquired results are compared to exact solutions to demonstrate the suggested method's effectiveness and reliability. Graphs and tables are used to display the numerical results. The results show that the natural decomposition technique is a very user-friendly and reliable method for dealing with fractional order nonlinear problems.

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