Homotopy Analysis Method for the Time-Fractional Boussinesq Equation

Abstract

In this paper, the exact and approximate analytical solutions to the time-fractional Boussinesq equation are constructed using the homotopy analysis method. Several examples about the fourth-order and sixth-order time-fractional Boussinesq equations show the flexibility and efficiency of the method. Furthermore, by choosing an appropriate value for the auxiliary parameter $h$, we can obtain the $N$-term approximate solution with improved accuracy.