Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives

Abstract

The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters $\alpha ,\beta$ in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.