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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 491359, 13 pages
http://dx.doi.org/10.1155/2013/491359
Research Article

The Extended Trial Equation Method for Some Time Fractional Differential Equations

1Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey
2Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey

Received 21 February 2013; Revised 25 March 2013; Accepted 14 April 2013

Academic Editor: Ferhan M. Atici

Copyright © 2013 Yusuf Pandir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.