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A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

Author

Listed:
  • M. Mossa Al-Sawalha

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

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA)

  • Rasool Shah

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

  • Osama Y. Ababneh

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Wajaree Weera

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

Abstract

In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems.

Suggested Citation

  • M. Mossa Al-Sawalha & Ravi P. Agarwal & Rasool Shah & Osama Y. Ababneh & Wajaree Weera, 2022. "A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas," Mathematics, MDPI, vol. 10(13), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2293-:d:852919
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    References listed on IDEAS

    as
    1. Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle & A. Ghareeb, 2022. "A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, Hindawi, vol. 2022, pages 1-30, February.
    2. Hassan Kamil Jassim, 2016. "The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-5, October.
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    Cited by:

    1. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.

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