Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By using a sequence of harmonic functions, we construct useful quantitative relation between the unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.