  Two Stefan's problems for the diffusion fractional equation are solved, where
the fractional derivative of order $ \al \in (0,1) $ is taken in the Caputo's
sense. The first one has a constant condition on $ x = 0 $ and the second
presents a flux condition $ T_x (0, t) = \frac {q} {t ^ {\al/2}} $. An
equivalence between these problems is proved and the convergence to the
classical solutions is analysed when $ \al \nearrow $ 1 recovering the heat
equation with its respective Stefan's condition.
