THE CALDERON PROBLEM FOR SPACE-TIME FRACTIONAL PARABOLIC OPERATORS WITH VARIABLE COEFFICIENTS

We study an inverse problem for variable coefficient fractional parabolic operators of the form (\partial t - 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 a 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.