In this thesis, we present a model for the free boundary Stefan problem. We begin with outlining the problem and its complexities, motivating the need for a numerical method. Then we introduce fractional operators, exploring various characteristics to narrow down the proper operator that will apply to the Stefan problem. We then outline our model, using the Caputo fractional derivative with a finite difference discretization and the SOR method to solve numerically. Our results are presented for different parameters such as latent heat and temperature. We end with suggestions for further work on our model
