Null controllability of a degenerate parabolic equation with delay

We are concerned about the null controllability of a linear degenerate parabolic equation with one delay parameter on the line $(0,1)$, where the control force is exerted on a subdomain of $(0,1)$ or on the boundary. For that we show how Carleman estimate can be used to establish such results. The second novelty, we discus the problem of boundary control for parabolic degenerate equations with delay.