Inverse problem of determining diffusion matrix between different structures for time fractional diffusion equation

In this paper we consider some inverse problems of determining the diffusion matrix between different structures for the time fractional diffusion equation featuring a Caputo derivative. We first study an inverse problem of determining the diffusion matrix in the period structure using data from the corresponding homogenized equation, then we investigate an inverse problem of determining the diffusion matrix in the homogenized equation using data from the corresponding period structure of the oscillating equation. Finally, we establish the stability and uniqueness for the first inverse problem, and the asymptotic stability for the second inverse problem.