We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by using the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results.

翻译：本文讨论从单点边界测量数据中识别时间分数阶扩散模型中的时变势函数问题。理论上，我们证明了该反问题的条件性Lipschitz稳定性。数值计算方面，我们提出了一种易于实现的迭代算法来恢复未知系数，并推导了离散重构的严格误差界。这些结果是通过利用正问题的（离散）解理论，并应用关于问题数据正则性最优的误差估计而获得的。数值模拟验证了理论结果。