New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method

Maysaa Al-Qurashi; Saima Rashid; Fahd Jarad; Madeeha Tahir; Abdullah M. Alsharif; Maysaa Al-Qurashi; Saima Rashid; Fahd Jarad; Madeeha Tahir; Abdullah M. Alsharif

doi:10.3934/math.2022117

AIMS Mathematics

2022, Volume 7, Issue 2: 2044-2060. doi: 10.3934/math.2022117

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Research article

New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method

1.
Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Çankaya University, Ankara, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Department of Mathematics, Government College Women University, Faisalabad, Pakistan
6.
Department of Mathematics, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 06 August 2021 Accepted: 24 October 2021 Published: 05 November 2021
MSC : 26A33, 26A51, 26D07, 26D10, 26D15

In this research, the Shehu transform is coupled with the Adomian decomposition method for obtaining the exact-approximate solution of the plasma fluid physical model, known as the Zakharov-Kuznetsov equation (briefly, ZKE) having a fractional order in the Caputo sense. The Laplace and Sumudu transforms have been refined into the Shehu transform. The action of weakly nonlinear ion acoustic waves in a plasma carrying cold ions and hot isothermal electrons is investigated in this study. Important fractional derivative notions are discussed in the context of Caputo. The Shehu decomposition method (SDM), a robust research methodology, is effectively implemented to generate the solution for the ZKEs. A series of Adomian components converge to the exact solution of the assigned task, demonstrating the solution of the suggested technique. Furthermore, the outcomes of this technique have generated important associations with the precise solutions to the problems being researched. Illustrative examples highlight the validity of the current process. The usefulness of the technique is reinforced via graphical and tabular illustrations as well as statistics theory.
- Shehu transform,
- Caputo fractional derivative,
- iterative transform method,
- Zakharov-Kuznetsov equation,
- analysis of variance
Citation: Maysaa Al-Qurashi, Saima Rashid, Fahd Jarad, Madeeha Tahir, Abdullah M. Alsharif. New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method[J]. AIMS Mathematics, 2022, 7(2): 2044-2060. doi: 10.3934/math.2022117

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Abstract

In this research, the Shehu transform is coupled with the Adomian decomposition method for obtaining the exact-approximate solution of the plasma fluid physical model, known as the Zakharov-Kuznetsov equation (briefly, ZKE) having a fractional order in the Caputo sense. The Laplace and Sumudu transforms have been refined into the Shehu transform. The action of weakly nonlinear ion acoustic waves in a plasma carrying cold ions and hot isothermal electrons is investigated in this study. Important fractional derivative notions are discussed in the context of Caputo. The Shehu decomposition method (SDM), a robust research methodology, is effectively implemented to generate the solution for the ZKEs. A series of Adomian components converge to the exact solution of the assigned task, demonstrating the solution of the suggested technique. Furthermore, the outcomes of this technique have generated important associations with the precise solutions to the problems being researched. Illustrative examples highlight the validity of the current process. The usefulness of the technique is reinforced via graphical and tabular illustrations as well as statistics theory.

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