  This paper deals with a theoretical mathematical analysis of a
one-dimensional-moving-boundary problem for the time-fractional diffusion
equation, where the time-fractional derivative of order $\al$ $\in (0,1)$ is
taken in the Caputo's sense. A generalization of the Hopf's lemma is proved,
and then this result is used to prove a monotonicity property for the
free-boundary when a fractional free-boundary Stefan problem is considered.
