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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 307371, 7 pages
http://dx.doi.org/10.1155/2014/307371
Research Article

A New Approach for Solving Fractional Partial Differential Equations in the Sense of the Modified Riemann-Liouville Derivative

School of Science, Shandong University of Technology, Zibo, Shandong 255049, China

Received 26 June 2014; Accepted 2 September 2014; Published 11 November 2014

Academic Editor: Alessandro Palmeri

Copyright © 2014 Bin Zheng and Qinghua Feng. 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

Based on a fractional complex transformation, certain fractional partial differential equation in the sense of the modified Riemann-Liouville derivative is converted into another ordinary differential equation of integer order, and the exact solutions of the latter are assumed to be expressed in a polynomial in Jacobi elliptic functions including the Jacobi sine function, the Jacobi cosine function, and the Jacobi elliptic function of the third kind. The degree of the polynomial can be determined by the homogeneous balance principle. With the aid of mathematical software, a series of exact solutions for the fractional partial differential equation can be found. For demonstrating the validity of this approach, we apply it to solve the space fractional KdV equation and the space-time fractional Fokas equation. As a result, some Jacobi elliptic functions solutions for the two equations are obtained.