Similarity solutions for phase change problems with fractional governing equations

In this paper, the scale-invariant solution of the fractional generalized Lame–Clapeyron–Stefan melting problem with a mushy region is considered. The time fractional heat conduction equations of orders α1α1 and α2α2 are used for the governing equations of the heat transfer in the liquid and solid phases. The Lie group method is used to determine the scale-invariant variables of the problem. To study the existence and characteristics of the similarity solutions, two cases α1≠α2α1≠α2 and α1=α2α1=α2 are discussed. The solutions are obtained in forms of generalized Wright function and the computations of these solutions are introduced in detail.