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Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Author

Listed:
  • Noufe H. Aljahdaly

    (Department of Mathematics, Faculty of Sciences and Arts, Rabigh Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ravi P. Agarwal

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

  • Rasool Shah

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

  • Thongchai Botmart

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

Abstract

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

Suggested Citation

  • Noufe H. Aljahdaly & Ravi P. Agarwal & Rasool Shah & Thongchai Botmart, 2021. "Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2326-:d:639021
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    References listed on IDEAS

    as
    1. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
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    Cited by:

    1. Doaa Atta & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    2. 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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