  In this article we study an inverse problem for the space-time fractional
parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space
dimension. We uniquely determine the unknown bounded potential $Q$ from
infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on
Runge approximation and the dual global weak unique continuation properties of
the equation under consideration. In discussing weak unique continuation of our
operator, a main feature of our argument relies on a Carleman estimate for the
associated fractional parabolic Caffarelli-Silvestre extension. Furthermore, we
also discuss constructive single measurement results based on the approximation
and unique continuation properties of the equation.
