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Exact Solutions for Some Fractional Differential Equations

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  • Abdullah Sonmezoglu

Abstract

The extended Jacobi elliptic function expansion method is used for solving fractional differential equations in the sense of Jumarie’s modified Riemann‐Liouville derivative. By means of this approach, a few fractional differential equations are successfully solved. As a result, some new Jacobi elliptic function solutions including solitary wave solutions and trigonometric function solutions are established. The proposed method can also be applied to other fractional differential equations.

Suggested Citation

  • Abdullah Sonmezoglu, 2015. "Exact Solutions for Some Fractional Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:567842
    DOI: 10.1155/2015/567842
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    References listed on IDEAS

    as
    1. Wei Li & Huizhang Yang & Bin He, 2014. "Exact Solutions of the Space‐Time Fractional Bidirectional Wave Equations Using the (G′/G)‐Expansion Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Wei Li & Huizhang Yang & Bin He, 2014. "Exact Solutions of the Space-Time Fractional Bidirectional Wave Equations Using the -Expansion Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, June.
    3. Bin Lu, 2014. "Bäcklund Transformation of Fractional Riccati Equation and Infinite Sequence Solutions of Nonlinear Fractional PDEs," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Song, Lina & Zhang, Hongqing, 2009. "Solving the fractional BBM–Burgers equation using the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1616-1622.
    5. Bin Lu, 2014. "Bäcklund Transformation of Fractional Riccati Equation and Infinite Sequence Solutions of Nonlinear Fractional PDEs," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
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