Numerical analysis of fractional-order Whitham-Broer-Kaup equations with non-singular kernel operators

M. Mossa Al-Sawalha; Osama Y. Ababneh; Rasool Shah; Amjad khan; Kamsing Nonlaopon; M. Mossa Al-Sawalha; Osama Y. Ababneh; Rasool Shah; Amjad khan; Kamsing Nonlaopon

doi:10.3934/math.2023120

AIMS Mathematics

2023, Volume 8, Issue 1: 2308-2336. doi: 10.3934/math.2023120

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Research article

Numerical analysis of fractional-order Whitham-Broer-Kaup equations with non-singular kernel operators

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
3.
Department of Mathematics, Abdul Wali khan university Mardan 23200, Pakistan
4.
Department of Mathematics and statistics, Bacha khan University, Palosa, Charsadda, Khyber Pakhtunkhwa, Pakistan
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 15 September 2022 Revised: 17 October 2022 Accepted: 19 October 2022 Published: 01 November 2022
MSC : 34A08, 35A20, 35R11

This paper solves a fractional system of non-linear Whitham-Broer-Kaup equations using a natural decomposition technique with two fractional derivatives. Caputo-Fabrizio and Atangana-Baleanu fractional derivatives were applied in a Caputo-manner. In addition, the results of the suggested method are compared to those of well-known analytical techniques such as the Adomian decomposition technique, the Variation iteration method, and the optimal homotopy asymptotic method. Two non-linear problems are utilized to demonstrate the validity and accuracy of the proposed methods. The analytical solution is then utilized to test the accuracy and precision of the proposed methodologies. The acquired findings suggest that the method used is very precise, easy to implement, and effective for analyzing the nature of complex non-linear applied sciences.
Citation: M. Mossa Al-Sawalha, Osama Y. Ababneh, Rasool Shah, Amjad khan, Kamsing Nonlaopon. Numerical analysis of fractional-order Whitham-Broer-Kaup equations with non-singular kernel operators[J]. AIMS Mathematics, 2023, 8(1): 2308-2336. doi: 10.3934/math.2023120

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Abstract

This paper solves a fractional system of non-linear Whitham-Broer-Kaup equations using a natural decomposition technique with two fractional derivatives. Caputo-Fabrizio and Atangana-Baleanu fractional derivatives were applied in a Caputo-manner. In addition, the results of the suggested method are compared to those of well-known analytical techniques such as the Adomian decomposition technique, the Variation iteration method, and the optimal homotopy asymptotic method. Two non-linear problems are utilized to demonstrate the validity and accuracy of the proposed methods. The analytical solution is then utilized to test the accuracy and precision of the proposed methodologies. The acquired findings suggest that the method used is very precise, easy to implement, and effective for analyzing the nature of complex non-linear applied sciences.

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