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The Extended Trial Equation Method for Some Time Fractional Differential Equations

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  • Yusuf Pandir
  • Yusuf Gurefe
  • Emine Misirli

Abstract

Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.

Suggested Citation

  • Yusuf Pandir & Yusuf Gurefe & Emine Misirli, 2013. "The Extended Trial Equation Method for Some Time Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-13, June.
    • Handle: RePEc:hin:jnddns:491359
    DOI: 10.1155/2013/491359
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    Cited by:

    1. Ozyapici, Ali & Bilgehan, Bülent, 2018. "Generalized system of trial equation methods and their applications to biological systems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 722-732.
    2. Liu, Cheng-shi, 2018. "Counterexamples on Jumarie’s three basic fractional calculus formulae for non-differentiable continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 219-222.

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