Numerical investigation of fractional-order wave-like equation

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

doi:10.3934/math.2023265

AIMS Mathematics

2023, Volume 8, Issue 3: 5281-5302. doi: 10.3934/math.2023265

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Research article

Numerical investigation of fractional-order wave-like equation

1.
Department of Mathematics, College 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, Khon Kaen University, Khon Kaen 40002, Thailand
4.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

Received: 03 September 2022 Revised: 28 November 2022 Accepted: 01 December 2022 Published: 14 December 2022
MSC : 32B15, 34A34, 35A22, 35A24, 45A10

The two approaches to solving nonlinear Caputo time-fractional wave-like equations with variable coefficients are examined in this study. The Homotopy perturbation transform method and the Yang transform decomposition method are the names of these two techniques. Three separate numerical examples are provided to demonstrate the effectiveness and precision of the suggested methods. The results were acquired to demonstrate the effectiveness and power of the two approaches, providing estimates with better precision and closed form solutions. The solutions to these kinds of equations can be found using the suggested methods as infinite series, and when these series are in closed form, they provide the exact solution. The suggested techniques have been demonstrated to be effective and efficient in their application. Three numerical examples are used to examine the methods accuracy and effectiveness.
- Homotopy perturbation method,
- Adomian decomposition method,
- Yang transform,
- nonlinear time-fractional wave-like equations,
- Caputo operator
Citation: M. Mossa Al-Sawalha, Rasool Shah, Kamsing Nonlaopon, Osama Y. Ababneh. Numerical investigation of fractional-order wave-like equation[J]. AIMS Mathematics, 2023, 8(3): 5281-5302. doi: 10.3934/math.2023265

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Abstract

The two approaches to solving nonlinear Caputo time-fractional wave-like equations with variable coefficients are examined in this study. The Homotopy perturbation transform method and the Yang transform decomposition method are the names of these two techniques. Three separate numerical examples are provided to demonstrate the effectiveness and precision of the suggested methods. The results were acquired to demonstrate the effectiveness and power of the two approaches, providing estimates with better precision and closed form solutions. The solutions to these kinds of equations can be found using the suggested methods as infinite series, and when these series are in closed form, they provide the exact solution. The suggested techniques have been demonstrated to be effective and efficient in their application. Three numerical examples are used to examine the methods accuracy and effectiveness.

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