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The Analysis of Fractional‐Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

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  • A. A. Alderremy
  • Shaban Aly
  • Rabia Fayyaz
  • Adnan Khan
  • Rasool Shah
  • Noorolhuda Wyal

Abstract

In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana–Baleanu fractional derivative operator are implemented to solve four systems. The obtained results by implementing the proposed methods are compared with exact solution. The convergence of the method is successfully presented and mathematically proved. The results we get are compared with exact solution through graphs and tables which confirms the effectiveness of the suggested techniques. In addition, the results obtained by employing the proposed approaches at different fractional orders are compared, confirming that as the value goes from fractional order to integer order, the result gets closer to the exact solution. Moreover, suggested techniques are interesting, easy, and highly accurate which confirm that these methods are suitable methods for solving any partial differential equations or systems of partial differential equations as well.

Suggested Citation

  • A. A. Alderremy & Shaban Aly & Rabia Fayyaz & Adnan Khan & Rasool Shah & Noorolhuda Wyal, 2022. "The Analysis of Fractional‐Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4935809
    DOI: 10.1155/2022/4935809
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    References listed on IDEAS

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    1. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    3. Hassan Khan & Adnan Khan & Maysaa Al-Qurashi & Rasool Shah & Dumitru Baleanu, 2020. "Modified Modelling for Heat Like Equations within Caputo Operator," Energies, MDPI, vol. 13(8), pages 1-14, April.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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