The main purpose of this thesis is to solve two special classes of nonlinear partial differential equations, the Allen-Cahn equation and the Burger-Fisher equation, using the fractional reduced differential transform method (FRDTM). We implement the proposed computational approach in some test problems. Also, we investigate the applicability and effectiveness of the presented method. At the first stage, the FRDTM is used to acquire approximate solutions of the time fractional-order diffusion equation and two special cases of Allen-Cahn equations. At the second stage, the FRDTM is used to evaluate the time-fractional generalized Burger-Fisher equation (TF-GBFE). To determine the validity of the method, when the solutions are obtained, they are compared to exact solutions of order α=1 , and even for various values of α. Three-dimensional graphs are used to depict the solutions. The analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.
