We investigate inverse problems in the determination of leading coefficients
for nonlocal parabolic operators, by knowing the corresponding Cauchy data in
the exterior space-time domain. The key contribution is that we reduce nonlocal
parabolic inverse problems to the corresponding local inverse problems with the
lateral boundary Cauchy data. In addition, we derive a new equation and offer a
novel proof of the unique continuation property for this new equation. We also
build both uniqueness and non-uniqueness results for both nonlocal isotropic
and anisotropic parabolic Calder\'on problems, respectively.Comment: 34 pages. All comments are welcom