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Abstract and Applied Analysis
Volume 2013, Article ID 426462, 8 pages
Research Article

Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

1Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics and Computer Science, 26480 Eskişehir, Turkey
2Dumlupınar University, School of Applied Sciences, Department of Management Information Systems, 43100 Kütahya, Turkey
3Yildiz Technical University, Education Faculty, Department of Mathematics Education, 34220 Istanbul, Turkey

Received 1 March 2013; Accepted 21 March 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Ahmet Bekir 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.


The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.