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

Author

Listed:
  • Meshari Alesemi

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

  • Naveed Iqbal

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

  • Thongchai Botmart

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

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.

Suggested Citation

  • Meshari Alesemi & Naveed Iqbal & Thongchai Botmart, 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:615-:d:751316
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    References listed on IDEAS

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    1. Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif & Dumitru Baleanu, 2019. "Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay," Mathematics, MDPI, vol. 7(6), pages 1-14, June.
    2. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

    1. Ahmed B. Khoshaim & Muhammad Naeem & Ali Akgul & Nejib Ghanmi & Shamsullah Zaland, 2022. "Novel Analysis of Fractional‐Order Fifth‐Order Korteweg–de Vries Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Rabab Alyusof & Shams Alyusof & Naveed Iqbal & Mohammad Asif Arefin, 2022. "Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel," Complexity, John Wiley & Sons, vol. 2022(1).
    3. Mohammed Kbiri Alaoui & Kamsing Nonlaopon & Ahmed M. Zidan & Adnan Khan & Rasool Shah, 2022. "Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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