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Exact Solutions of the Space‐Time Fractional Bidirectional Wave Equations Using the (G′/G)‐Expansion Method

Author

Listed:
  • Wei Li
  • Huizhang Yang
  • Bin He

Abstract

Based on Jumarie’s modified Riemann‐Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations. Exact solutions including the hyperbolic functions, the trigonometric functions, and the rational functions for the space‐time fractional bidirectional wave equations are obtained using the (G′/G)‐expansion method. The method provides a promising tool for solving nonlinear fractional differential equations.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:153706
    DOI: 10.1155/2014/153706
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    References listed on IDEAS

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    1. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, May.
    2. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, November.
    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. Ahmet Bekir & Özkan Güner & Adem C. Cevikel, 2013. "Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, June.
    5. Fanwei Meng, 2013. "A New Approach for Solving Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. 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.
    7. Ahmet Bekir & Özkan Güner & Adem C. Cevikel, 2013. "Fractional Complex Transform and exp‐Function Methods for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Ali Akgül & Adem Kılıçman & Mustafa Inc, 2013. "Improved (G′/G)‐Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    10. Ali Akgül & Adem Kılıçman & Mustafa Inc, 2013. "Improved ( )-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, September.
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    Cited by:

    1. Abdullah Sonmezoglu, 2015. "Exact Solutions for Some Fractional Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).

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