In this paper, we apply the improved Kudryashov method for finding exact solution and then solitary wave solutions of the Chafee-Infante equation and (2+1)-dimensional breaking soliton equation, where mathematical software Maple-13 is used as an important mathematical tool for removing calculation complexity, justification of the solutions and its graphical representations.

Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this method and we get some new travelling wave solutions. To acquire our purpose a complex transformation has been also used to reduce nonlinear fractional partial differential equations to nonlinear ordinary differential equations of integer order, in the sense of the Jumarie's modified Riemann-Liouville derivative. Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13.

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Abstract. In this work, the generalized ) ) ( exp( ξ ϕ -expansion method is used to find traveling wave solutions of Korteweg-de Varies equation (KdV) and modified Liouville equation. This method gives travelling wave solutions and finally solitary wave solutions with respective graphs. The generalized − )) ( exp( ξ ϕ expansion method is very powerful and convenient mathematical tool for finding the exact solutions of nonlinear evolution equations arise in science and engineering.