Hindawi Publishing Corporation International Journal of Differential Equations Volume 2010, Article ID 954674, 11 pages doi:10.1155/2010/954674 Research Article Solitary Wave Solutions for a Time-Fraction Generalized Hirota-Satsuma Coupled KdV Equation by a New Analytical Technique Majid Shateri and D. D. Ganji Department of Mechanical Engineering, Babol University of Technology, P.O. Box 484, 47148 71167 Babol, Iran Correspondence should be addressed to D. D. Ganji, ddg davood@yahoo.com Received 17 May 2009; Accepted 7 July 2009 Academic Editor: Shaher Momani Copyright q 2010 M. Shateri and D. D. Ganji. 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. A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the limitations of these methods. The obtained numerical results show good agreement with those of analytical solutions. The fractional derivatives are described in Caputo sense. 1. Introduction In recent years, it has been turned out that fractional differential equations can be used successfully to model many phenomena in various fields such as fluid mechanics, viscoelasticity, physics, chemistry, and engineering. For instance, the fluid-dynamics traffic model with fractional derivatives 1 is able to eliminate the deficiency arising from the assumption of continuum traffic flow, and the nonlinear oscillation of earthquakes can be modeled by fractional derivatives 2. Fractional differentiation and integration operators can also be used for extending the diffusion and wave equations 3. Most of fractional differential equations do not have exact analytical solutions, hence considerable heed has been focused on the approximate and numerical solutions of these equations. Although variational iteration method 4-8 and Adomian’s decomposition method 9-14 are approaches that have been utilized extensively to provide analytical approximations of linear and nonlinear problems, they have limitations due to complicated algorithms of calculating Adomian polynomials for nonlinear fractional problems, and an inherent inaccuracy in determining