On a Fractional Diffusion Equation with Moving Control

This article considers a one-dimensional fractional parabolic equation, which may serve as a mathematical model for anomalous diffusion phenomena. It is known that, if the support of the control is fixed, this equation is not even spectrally controllable. We show that, when the control support is shifted in time with constant velocity $c$, the system is null-controllable in a sufficiently large time depending on $c$.