Approximate Solutions for Time-Fractional Fornberg–Whitham Equation with Variable Coefficients

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and 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 classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable coefficients. We consider homogeneous boundary conditions find solutions bounded space l<χ<L l,L∈R. To confirm effectiveness proposed methods non-integer η, computation two test problems was presented. A comparison made between results (VIM), (ADM), (HAM) through tables graphs. demonstrate methods.