Uniqueness of the potential in a time-fractional diffusion equation

Abstract

Abstract This article concerns the uniqueness of an inverse coefficient problem of identifying a spatially varying potential in a one-dimensional time-fractional diffusion equation. The input sources are given by a complete system in L 2 ⁢ ( 0 , 1 ) {L^{2}(0,1)} , and measurements are observed at the end point of the spatial interval. Firstly, we provide the positive lower bound of the Green function for the differential operator with different boundary conditions. Then, based on the positive lower bound estimation of the Green function, the relationship between the Green function, the solution of the forward problem, and the potential, such measurements uniquely determine the potential on the entire interval under different boundary conditions.