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

On the time fractional heat equation with obstacle