  We consider the homogenization for time-fractional diffusion equations in a
periodic structure and we derive the homogenized time-fractional diffusion
equation. Then we discuss the determination of the constant diffusion
coefficient by minimum data. Combining the results obtained above, we
investigate the inverse problems of determining the diffusion coefficient for
the homogenized equations from the data in the periodic structure and vice
versa, that is, we investigate the inverse problem of determining the diffusion
coefficient for the periodic equations from the data in the homogenized
structure.
