  Two fractional two-phase Stefan-like problems are considered by using
Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying
that they coincide with the same classical Stefan problem at the limit case
when $\alpha=1$. For both problems, explicit solutions in terms of the Wright
functions are presented. Even though the similarity of the two solutions, a
proof that they are different is also given. The convergence when $\alpha
\nearrow 1$ of the one and the other solutions to the same classical solution
is given. Numerical examples for the dimensionless version of the problem are
also presented and analyzed.
