Evaluation of time-fractional Fisher's equations with the help of analytical methods

Ahmed M. Zidan; Adnan Khan; Rasool Shah; Mohammed Kbiri Alaoui; Wajaree Weera; Ahmed M. Zidan; Adnan Khan; Rasool Shah; Mohammed Kbiri Alaoui; Wajaree Weera

doi:10.3934/math.20221031

AIMS Mathematics

2022, Volume 7, Issue 10: 18746-18766. doi: 10.3934/math.20221031

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Evaluation of time-fractional Fisher's equations with the help of analytical methods

1.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, 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

Received: 23 May 2022 Revised: 04 August 2022 Accepted: 09 August 2022 Published: 23 August 2022
MSC : 34A34, 35A20, 35A22, 44A10, 33B15

This article shows how to solve the time-fractional Fisher's equation through the use of two well-known analytical methods. The techniques we propose are a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform. To show the accuracy of the suggested techniques, illustrative examples are considered. It is confirmed that the solution we get by implementing the suggested techniques has the desired rate of convergence towards the accurate solution. The main benefit of the proposed techniques is the small number of calculations. To show the reliability of the suggested techniques, we present some graphical behaviors of the accurate and analytical results, absolute error graphs and tables that strongly agree with each other. Furthermore, it can be used for solving fractional-order physical problems in various fields of applied sciences.
- Yang transform decomposition method,
- homotopy perturbation Yang transform method,
- time-fractional Fisher's equation,
- Caputo operator
Citation: Ahmed M. Zidan, Adnan Khan, Rasool Shah, Mohammed Kbiri Alaoui, Wajaree Weera. Evaluation of time-fractional Fisher's equations with the help of analytical methods[J]. AIMS Mathematics, 2022, 7(10): 18746-18766. doi: 10.3934/math.20221031

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Abstract

This article shows how to solve the time-fractional Fisher's equation through the use of two well-known analytical methods. The techniques we propose are a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform. To show the accuracy of the suggested techniques, illustrative examples are considered. It is confirmed that the solution we get by implementing the suggested techniques has the desired rate of convergence towards the accurate solution. The main benefit of the proposed techniques is the small number of calculations. To show the reliability of the suggested techniques, we present some graphical behaviors of the accurate and analytical results, absolute error graphs and tables that strongly agree with each other. Furthermore, it can be used for solving fractional-order physical problems in various fields of applied sciences.

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