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

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 η=(0,1] with variable coefficients. We consider homogeneous boundary conditions to find the approximate solutions for the bounded space variable l<χ<L and l,L∈R. To confirm the effectiveness of the proposed methods of non-integer order η, 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.