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An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations

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)

Abstract

The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional derivatives. Some illustrative examples are considered to check the validity and accuracy of the proposed method. The obtained results have shown the best agreement with the exact solution for the problems. The solution graphs are in full support to confirm the authenticity of the present method.

Suggested Citation

  • Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif, 2019. "An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:505-:d:236651
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    References listed on IDEAS

    as
    1. Muhammad Jibran & Rashid Nawaz & Asfandyar Khan & Sajjad Afzal, 2018. "Iterative Solutions of Hirota Satsuma Coupled KDV and Modified Coupled KDV Systems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-18, December.
    2. Helal, M.A. & Mehanna, M.S., 2007. "A comparative study between two different methods for solving the general Korteweg–de Vries equation (GKdV)," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 725-739.
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    Cited by:

    1. A. A. Alderremy & Hassan Khan & Rasool Shah & Shaban Aly & Dumitru Baleanu, 2020. "The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
    2. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.

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