Abstract
The aim of this paper is to describe the new fractional Temimi-Ansari method (FTAM) for the KdV-Burgers equation and the Benjamin-Bona-Mahoney-Burger equation (BBMB) with time fractional order. Convergence of the presented method has been successfully achieved. This method does not need any assumptions for nonlinear terms. FTAM with time fractional order is demonstrated to be a very simple and effective approach to solving nonlinear fractional problems. The accuracy and efficiency of FTAM has been demonstrated by studying the convergence of this technique.