  We review some fractional free boundary problems that were recently
considered for modeling anomalous phase-transitions. All problems are of Stefan
type and involve fractional derivatives in time according to Caputo's
definition. We survey the assumptions from which they are obtained and observe
that the problems are nonequivalent though all of them reduce to a classical
Stefan problem when the order of the fractional derivatives is replaced by one.
We further show that a simple heuristic approach built upon a fractional
version of the energy balance and the classical Fourier's law leads to a
natural generalization of the classical Stefan problem in which time
derivatives are replaced by fractional ones.
