On the time fractional heat equation with obstacle

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