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Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay

Author

Listed:
  • Rasool Shah

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

  • Hassan Khan

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

  • Poom Kumam

    (Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Muhammad Arif

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

  • Dumitru Baleanu

    (Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey)

Abstract

In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. Natural transform decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. Therefore, Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear Partial deferential equations particularly fractional-order partial differential equations with proportional delay.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:532-:d:238835
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    Citations

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    Cited by:

    1. 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.
    2. Liaqat, Muhammad Imran & Khan, Adnan & Akgül, Ali, 2022. "Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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