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The modified simple equation method and the multiple exp-function method for solving nonlinear fractional Sharma-Tasso-Olver equation

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Abstract

In this article, the fractional derivatives in the sense of the modified Riemann-Liouville derivatives together with the modified simple equation method and the multiple exp-function method are employed for constructing the exact solutions and the solitary wave solutions for the nonlinear time fractional Sharma-Tasso- Olver equation. With help of Maple, we can get exact explicit 1-wave, 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions if we use the multiple exp-function method while we can get only exact explicit 1-wave solution including 1-soliton type solution if we use the modified simple equation method. Two cases with specific values of the involved parameters are plotted for each 2-wave and 3-wave solutions.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Sciences, Zagazig University, Zagazig, Egypt

    Elsayed M. E. Zayed & Yaser A. Amer

  2. Mathematics Department, Faculty of Education, Ain Shams University, Roxy, Hiliopolis, Cairo, Egypt

    Abdul-Ghani Al-Nowehy

Authors
  1. Elsayed M. E. Zayed
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  2. Yaser A. Amer
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  3. Abdul-Ghani Al-Nowehy
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Correspondence to Elsayed M. E. Zayed.

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Zayed, E.M.E., Amer, Y.A. & Al-Nowehy, AG. The modified simple equation method and the multiple exp-function method for solving nonlinear fractional Sharma-Tasso-Olver equation. Acta Math. Appl. Sin. Engl. Ser. 32, 793–812 (2016). https://doi.org/10.1007/s10255-016-0590-9

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  • DOI: https://doi.org/10.1007/s10255-016-0590-9

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