Author(s)

Ogugua N. Onyejekwe

Department of Mathematics, Indian River State College, Fort Pierce, FL, USA.

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.

Diffusion Equation, Fractional Derivatives, Homotopy Analysis Method, Moving Boundary

Onyejekwe, O. (2025) Homotopy Analysis Method Solution to Time-Fractional Diffusion with a Moving Boundary. Journal of Applied Mathematics and Physics, 13, 2090-2096. doi: 10.4236/jamp.2025.136116.