Evaluation of fractional-order equal width equations with the exponential-decay kernel

Manal Alqhtani; Khaled M. Saad; Rasool Shah; Thongchai Botmart; Waleed M. Hamanah; Manal Alqhtani; Khaled M. Saad; Rasool Shah; Thongchai Botmart; Waleed M. Hamanah

doi:10.3934/math.2022949

AIMS Mathematics

2022, Volume 7, Issue 9: 17236-17251. doi: 10.3934/math.2022949

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Evaluation of fractional-order equal width equations with the exponential-decay kernel

1.
Department of Mathematics, College of Sciences and Arts, Najran University, Najran, Kingdom of Saudi Arabia
2.
Department of Mathematics, Abdul Wali Khan University Mardan Pakistan
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
4.
Interdisciplinary Research Center in Renewable Energy and Power Systems, King Fahd University for Petroleum and Minerals, P.O. Box 5028, Dhahran 31261, Saudi Arabia

Received: 09 June 2022 Revised: 06 July 2022 Accepted: 15 July 2022 Published: 22 July 2022
MSC : 34A34, 35A20, 35A22, 44A10, 33B15

In this article we consider the homotopy perturbation transform method to investigate the fractional-order equal-width equations. The homotopy perturbation transform method is a mixture of the homotopy perturbation method and the Yang transform. The fractional-order derivative are defined in the sense of Caputo-Fabrizio operator. Several fractions of solutions are calculated which define some valuable evolution of the given problems. The homotopy perturbation transform method results are compared with actual results and good agreement is found. The suggested method can be used to investigate the fractional perspective analysis of problems in a variety of applied sciences.
- homotopy perturbation method,
- Yang transform,
- equal width equations,
- Caputo-Fabrizio operator
Citation: Manal Alqhtani, Khaled M. Saad, Rasool Shah, Thongchai Botmart, Waleed M. Hamanah. Evaluation of fractional-order equal width equations with the exponential-decay kernel[J]. AIMS Mathematics, 2022, 7(9): 17236-17251. doi: 10.3934/math.2022949

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Abstract

In this article we consider the homotopy perturbation transform method to investigate the fractional-order equal-width equations. The homotopy perturbation transform method is a mixture of the homotopy perturbation method and the Yang transform. The fractional-order derivative are defined in the sense of Caputo-Fabrizio operator. Several fractions of solutions are calculated which define some valuable evolution of the given problems. The homotopy perturbation transform method results are compared with actual results and good agreement is found. The suggested method can be used to investigate the fractional perspective analysis of problems in a variety of applied sciences.

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