A Study of a Stefan Problem Governed With Space–Time Fractional Derivatives

This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a position’s latent-heat power function. This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained using the optimal homotopy asymptotic method to find approximate solutions of temperature distribution in the domain and using the interface’s tracking or location. The results thus obtained are compared with existing exact solutions for the case of the integer order derivative at some particular values of the governing parameters. A study also is performed of the interface movement’s dependence on certain parameters.