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The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations

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  • Bin Zheng
  • Qinghua Feng

Abstract

Based on a nonlinear fractional complex transformation, the Jacobi elliptic equation method is extended to seek exact solutions for fractional partial differential equations in the sense of the modified Riemann‐Liouville derivative. For demonstrating the validity of this method, we apply it to solve the space fractional coupled Konopelchenko‐Dubrovsky (KD) equations and the space‐time fractional Fokas equation. As a result, some exact solutions for them including the hyperbolic function solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic function solutions are successfully found.

Suggested Citation

  • Bin Zheng & Qinghua Feng, 2014. "The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:249071
    DOI: 10.1155/2014/249071
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, May.
    3. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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