Abstract
In this research, three numerical methods, namely the variational iteration method, the Adomian decomposition method, and the homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from the classical (FW) equation by replacing the integer-order time derivative with the Caputo fractional derivative of order ? = (0,1] with variable coefficients. We consider homogeneous boundary conditions to find the approximate solutions for the bounded space variable l < ? < L and l, L ? R. To confirm the effectiveness of the proposed methods of non-integer order ?, the computation of two test problems was presented. A comparison is made between the obtained results of the (VIM), (ADM), and (HAM) through tables and graphs. The numerical results demonstrate the effectiveness of the three numerical methods.