Modeling of freezing processes by an one-dimensional thermal conductivity equation with fractional differentiation operators

We have studied the Stefan problem with Caputo fractional order time derivatives. The difference scheme is built. The algorithm and the program for a numerical solution of the Stefan problem with fractional differentiation operator are created. For the given entry conditions and freezing ground parameters we have obtained the space-time temperature dependences for different values of parameter $\alpha $. The functional dependences of the interface motion for the generalized Stefan conditions depending on the value of $\alpha $ are estimated. Finally we have found that the freezing process is slowed down during the transition to fractional derivatives.