Homotopy perturbation method to space–time fractional solidification in a finite slab

A mathematical model describing the space and time fractional solidification of fluid initially at its freezing temperature contained in a finite slab under the constant wall temperature is presented. The approximate analytical solution of this problem is obtained by the homotopy perturbation method. The results thus obtained are compared with exact solution of integer order (β = 1, α = 2) and are good agreement. The problem has been studied in detail by considering different order time and space fractional derivatives. The temperature distribution and the moving interface position for different fractional order space and time derivatives are shown graphically. The model and the solution are the generalization of the previous works and include them as special cases.