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Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

Author

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  • Gang wei Wang
  • Tian zhou Xu
  • Tao Feng

Abstract

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided.

Suggested Citation

  • Gang wei Wang & Tian zhou Xu & Tao Feng, 2014. "Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-6, February.
    • Handle: RePEc:plo:pone00:0088336
    DOI: 10.1371/journal.pone.0088336
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    Cited by:

    1. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    2. Zhang, Yufeng & Mei, Jianqin & Zhang, Xiangzhi, 2018. "Symmetry properties and explicit solutions of some nonlinear differential and fractional equations," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 408-418.
    3. Ali H Bhrawy & Taha M Taha & Ebrahim O Alzahrani & Dumitru Baleanu & Abdulrahim A Alzahrani, 2015. "New Operational Matrices for Solving Fractional Differential Equations on the Half-Line," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-23, May.

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