Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel

Alesemi, Meshari; Iqbal, Naveed; Botmart, Thongchai

doi:10.3390/math10040615

Open AccessArticle

Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel

by

Meshari Alesemi

¹

,

Naveed Iqbal

²

and

Thongchai Botmart

^3,*

¹

Department of Mathematics, College of Science, University of Bisha, P.O. Box 511, Bisha 61922, Saudi Arabia

²

Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

³

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(4), 615; https://doi.org/10.3390/math10040615

Submission received: 28 January 2022 / Revised: 10 February 2022 / Accepted: 14 February 2022 / Published: 17 February 2022

(This article belongs to the Special Issue Computational, Experimental, and Theoretical Aspect of Fractional Order Operators)

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Abstract

This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution.

Keywords: variational iterative method; Caputo–Fabrizio derivative; Yang transform; homotopy perturbation method; polytropic gas equation

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MDPI and ACS Style

Alesemi, M.; Iqbal, N.; Botmart, T. Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel. Mathematics 2022, 10, 615. https://doi.org/10.3390/math10040615

AMA Style

Alesemi M, Iqbal N, Botmart T. Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel. Mathematics. 2022; 10(4):615. https://doi.org/10.3390/math10040615

Chicago/Turabian Style

Alesemi, Meshari, Naveed Iqbal, and Thongchai Botmart. 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel" Mathematics 10, no. 4: 615. https://doi.org/10.3390/math10040615

APA Style

Alesemi, M., Iqbal, N., & Botmart, T. (2022). Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel. Mathematics, 10(4), 615. https://doi.org/10.3390/math10040615

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel

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