Uniqueness for fractional nonsymmetric diffusion equations and an application to an inverse source problem

Abstract

In this article, we discuss a solution to time‐fractional diffusion equation with the homogeneous Dirichlet boundary condition, where an elliptic operator is not necessarily symmetric. We prove that the solution is identically zero if its normal derivative with respect to the operator vanishes on an arbitrarily chosen subboundary of the spatial domain over a time interval. The proof is based on the Laplace transform and the spectral decomposition for a nonsymmetric elliptic operator. As a direct application, we prove the uniqueness result for an inverse problem on determining the spatial component in the source term by Neumann boundary data on subdoundary.