Homotopy Analysis Method Solution to Time-Fractional Diffusion with a Moving Boundary

It is difficult to obtain exact or analytical solutions to most moving boundary problems. In this paper, we employ the use of Homotopy Analysis Method (HAM) to solve a time-fractional diffusion equation with a moving boundary. HAM is a semi-analytic technique used to solve ordinary, partial, algebraic, delay and fractional differential equations. This method uses the concept of homotopy from topology to generate a convergent series solution for nonlinear systems. The homotopy Maclaurin series is utilized to deal with nonlinearities in the system.