Lipschitz regularity for the parabolic $(s,p)-$obstacle problem

We study the obstacle problem for the parabolic fractional $p-$Laplace equation $${\mathrm{\partial }}_{t}u+(-{\mathrm{\Delta }}_p{)}^{s}u=0$$ in the degenerate range $2<p<2\mathrm{/}(1-s)$. We prove that viscosity solutions are locally Lipschitz continuous in space and Hölder continuous in time. If, in addition, $p>1\mathrm{/}(1-s)$, the time regularity improves to Lipschitz continuity.