a study of a stefan problem governed with space–time fractional derivatives

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate solutions of temperature distribution in the given domain and tracking or location of interface. the results thus obtained are compared with existing exact solutions for the case of integer ordered derivative at some particular values of the governing parameters. it is found that the obtained results are sufficiently closed to the exact solution of the problem. a study of variations of thermal diffusion coefficient in the case of fractional ordered derivatives is discussed. moreover, we discussed the dependence of movement of interface on some parameters used in the mathematical model of the problem.