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 α. 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.

我们考虑具有阶数时间分数阶导数的一维扩散方程的初始边值问题$\alpha \in (0,\mathrm{1个})$这是受非零诺伊曼边界条件。我们通过狄利克雷数据在空间区间的一个端点证明了确定空间变化势和时间分数阶导数的逆系数问题的唯一性。强加的诺伊曼条件需要在正确的α阶 Sobolev 空间内。我们的证明基于具有非零边界数据的初始边界值问题的解的表示公式。此外，我们应用这样一个公式，证明了用一个端点的柯西数据确定另一个端点边界值的唯一性。