Simultaneous uniqueness in determining the space-dependent coefficient and source for a time-fractional diffusion equation

This article concerns the uniqueness of an inverse problem of simultaneously identifying the space-dependent coefficient and source in a one-dimensional time-fractional diffusion equation with derivative order alpha is an element of(0,1)$$ \alpha \in \left(0,1\right) $$ and the zero Neumann boundary value. By additional boundary measurements, we first obtain the uniqueness of the coefficient from the Laplace transform and a transformation formula. Then, we further show the uniqueness of the source through the asymptotic behavior of solutions to the corresponding forward problem. The result shows that the uniqueness of the simultaneous identification can be obtained under the condition that the prior information only on one set of parameters in the model is given other than that of two sets.