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A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

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Listed:
  • Shuang-Shuang Zhou

    (College of Science, Hunan City University, Yiyang 413000, China)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea)

  • Ioannis Dassios

    (AMPSAS, University College Dublin, D04 V1W8 Dublin, Ireland)

  • S. Saleem

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Kamsing Nonlaopon

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

Abstract

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

Suggested Citation

  • Shuang-Shuang Zhou & Nehad Ali Shah & Ioannis Dassios & S. Saleem & Kamsing Nonlaopon, 2021. "A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques," Mathematics, MDPI, vol. 9(15), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1735-:d:599597
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    References listed on IDEAS

    as
    1. 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. Victor V. Kuzenov & Sergei V. Ryzhkov & Aleksey Yu. Varaksin, 2022. "The Adaptive Composite Block-Structured Grid Calculation of the Gas-Dynamic Characteristics of an Aircraft Moving in a Gas Environment," Mathematics, MDPI, vol. 10(12), pages 1-14, June.

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