  We study the isotropization and thermalization of heavy quarks in a
non-Markovian medium in high energy nuclear collisions. In particular, we
analyze the case of a non-stationary medium with a noise whose time-correlator
decays as a power law (heavy tailed noise). We assume the correlations decay
with an exponent $\beta-1$, $0\leq\beta<1$; we treat $\beta$ as a free
parameter. We analyze the effect of memory on the thermalization and
isotropization of heavy quarks in the medium via a generalized Langevin
equation. In general, we find that memory slows down the dynamics of heavy
quarks; moreover, thermalization and isotropization happen on the same time
scale once a realistic initialization is considered. We also find that while
the effect on charm quarks can be relevant, beauty quarks are hardly affected
by memory in the quark-gluon plasma phase. Finally, we comment on the effect of
memory on the estimate of $D_s$ of charm and beauty.
