  In this paper, we consider the direct and inverse problem for time-fractional
diffusion in a domain with an impenetrable subregion. Here we assume that on
the boundary of the subregion the solution satisfies a generalized impedance
boundary condition. This boundary condition is given by a second order spacial
differential operator imposed on the boundary. A generalized impedance boundary
condition can be used to model corrosion and delimitation. The well-posedness
for the direct problem is established where the Laplace Transform is used to
study the time dependent boundary value problem. The inverse impedance problem
of determining the parameters from the Cauchy data is also studied provided the
boundary of the subregion is known. The uniqueness of recovering the boundary
parameters from the Neumann to Dirichlet mapping is proven.
