  We study an inverse problem for variable coefficient fractional parabolic
operators of the form $(\partial_t -\operatorname{div}(A(x) \nabla_x)^s +
q(x,t)$ for $s\in(0,1)$ and show the unique recovery of $q$ from exterior
measured data. Similar to the fractional elliptic case, we use Runge type
approximation argument which is obtained via a global weak unique continuation
property. The proof of such a unique continuation result involves a new
Carleman estimate for the associated variable coefficient extension operator.
In the latter part of the work, we prove analogous unique determination results
for fractional parabolic operators with drift.
