  We consider initial boundary value problems for one-dimensional diffusion
equation with time-fractional derivative of order $\alpha \in (0,1)$ which are
subject to non-zero Neumann boundary conditions. We prove the uniqueness for an
inverse coefficient problem of determining a spatially varying potential and
the order of the time-fractional derivative by Dirichlet data at one end point
of the spatial interval. The imposed Neumann conditions are required to be
within the correct Sobolev space of order $\alpha$. Our proof is based on a
representation formula of solution to an initial boundary value problem with
non-zero boundary data. Moreover, we apply such a formula and prove the
uniqueness in the determination of boundary value at another end point by
Cauchy data at one end point.
