  We consider a rather general class of non-local in time Fokker-Planck
equations and show by means of the entropy method that as $t\to \infty$ the
solution converges in $L^1$ to the unique steady state. Important special cases
are the time-fractional and ultraslow diffusion case. We also prove estimates
for the rate of decay. In contrast to the classical (local) case, where the
usual time derivative appears in the Fokker-Planck equation, the obtained decay
rate depends on the entropy, which is related to the integrability of the
initial datum. It seems that higher integrability of the initial datum leads to
better decay rates and that the optimal decay rate is reached, as we show, when
the initial datum belongs to a certain weighted $L^2$ space. We also show how
our estimates can be adapted to the discrete-time case thereby improving known
decay rates from the literature.
