Residual power series method for the time fractional Fornberg-Whitham equation

Abstract

The purpose of this paper is to solve the time fractional Fornberg-Whitham equation by the residual power series method, where the fractional derivatives are in Caputo sense. According to the definition of generalised fractional power series, the solutions of the fractional differential equations are approximatively expanded and substituted into the differential equations. The coefficients to be determined in the approximate solutions are calculated according to the residual functions and the initial conditions, and the approximate analytical solutions of the equations can be obtained. Finally, the approximate analytical solutions are compared with the exact solutions. The results show that the residual power series method is convenient and effective for solving the time fractional Fornberg-Whitham equation.