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Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method

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  • Jianke Zhang
  • Zhirou Wei
  • Longquan Yong
  • Yuelei Xiao

Abstract

In this study, a generalized Taylor series formula together with residual error function, which is named the residual power series method (RPSM), is used for finding the series solution of the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The BBM-Burger equation is useful in describing approximately the unidirectional propagation of long waves in certain nonlinear dispersive systems. The numerical solution of the BBM-Burger equation is calculated by Maple. The numerical results show that the RPSM is reliable and powerful in solving the numerical solutions of the BBM-Burger equation compared with the exact solutions as well as the solutions obtained by homotopy analysis transform method through different graphical representations and tables.

Suggested Citation

  • Jianke Zhang & Zhirou Wei & Longquan Yong & Yuelei Xiao, 2018. "Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method," Complexity, Hindawi, vol. 2018, pages 1-11, October.
    • Handle: RePEc:hin:complx:2891373
    DOI: 10.1155/2018/2891373
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    Cited by:

    1. Jianke Zhang & Zhirou Wei & Lifeng Li & Chang Zhou, 2019. "Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations," Complexity, Hindawi, vol. 2019, pages 1-15, October.

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