  We study a Caputo time fractional degenerate diffusion equation which we
prove to be equivalent to the fractional parabolic obstacle problem, showing
that its solution evolves for any $\alpha\in(0,1)$ to the same stationary
state, the solution of the classic elliptic obstacle problem. The only thing
which changes with $\alpha$ is the convergence speed. We also study the problem
from the numerical point of view, comparing some finite different approaches,
and showing the results of some tests. These results extend what recently
proved in [1] for the case $\alpha=1$.
