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In this paper, we use the fractional complex transform and the (G /G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.

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.

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In this paper, we establish exact solutions for nonlinear equations. The sine-cosine method is used to construct periodic and soliton solutions of nonlinear physical models. Many new families of exact travelling wave solutions of the symmetric regularized long-wave (SRLW) and the Klein-Gordon-Zakharov (KGZ) equations are successfully obtained. These solutions may be important for the explanation of some practical physical problems. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.