Fractional view evaluation system of Schrödinger-KdV equation by a comparative analysis

Rasool Shah; Abd-Allah Hyder; Naveed Iqbal; Thongchai Botmart; Rasool Shah; Abd-Allah Hyder; Naveed Iqbal; Thongchai Botmart

doi:10.3934/math.20221087

AIMS Mathematics

2022, Volume 7, Issue 11: 19846-19864. doi: 10.3934/math.20221087

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Fractional view evaluation system of Schrödinger-KdV equation by a comparative analysis

1.
Department of Mathematics, Abdul Wali khan university Mardan 23200, Pakistan
2.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
3.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt
4.
Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 15 June 2022 Revised: 23 August 2022 Accepted: 30 August 2022 Published: 08 September 2022
MSC : 34A34, 35A20, 35A22, 44A10, 33B15

The time-fractional coupled Schrödinger-KdV equation is an interesting mathematical model because of its wide and significant application in mathematics and applied sciences. A fractional coupled Schrödinger-KdV equation in the sense of Caputo derivative is investigated in this article. Namely, we provide a comparative study of the considered model using the Adomian decomposition method and the homotopy perturbation method with Shehu transform. Approximate solutions obtained using the Adomian decomposition and homotopy perturbation methods were numerically evaluated and presented in graphs and tables. Then, these solutions were compared to the exact solutions, demonstrating the simplicity, effectiveness, and good accuracy of the applied method. To demonstrate the accuracy and efficiency of the suggested techniques, numerical problem are provided.
- homotopy perturbation Shehu transform,
- Adomian decomposition method,
- coupled Schrödinger-KdV equation,
- Caputo fractional operator
Citation: Rasool Shah, Abd-Allah Hyder, Naveed Iqbal, Thongchai Botmart. Fractional view evaluation system of Schrödinger-KdV equation by a comparative analysis[J]. AIMS Mathematics, 2022, 7(11): 19846-19864. doi: 10.3934/math.20221087

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Abstract

The time-fractional coupled Schrödinger-KdV equation is an interesting mathematical model because of its wide and significant application in mathematics and applied sciences. A fractional coupled Schrödinger-KdV equation in the sense of Caputo derivative is investigated in this article. Namely, we provide a comparative study of the considered model using the Adomian decomposition method and the homotopy perturbation method with Shehu transform. Approximate solutions obtained using the Adomian decomposition and homotopy perturbation methods were numerically evaluated and presented in graphs and tables. Then, these solutions were compared to the exact solutions, demonstrating the simplicity, effectiveness, and good accuracy of the applied method. To demonstrate the accuracy and efficiency of the suggested techniques, numerical problem are provided.

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