In this work, we study an inverse problem of recovering information about the weight distribution in a distributed-order time-fractional diffusion model from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of the involved problem data, we prove that the one-point observation can uniquely determine the support of the weight distribution. The proof is based on asymptotic behavior of the measurement as well as analytic continuation and Titchmarch convolution theorem. In addition, when the problem data are fully known, we give an alternative proof of an existing result, which states that the over-posed one-point boundary observation can uniquely determine the weight. Several numerical experiments are presented to complement the theoretical analysis.

翻译：在这项工作中,我们研究一个反向问题,即从在域边界某一点的观察中,从某一点的观察中找到关于分布顺序时间折射扩散模型中重量分布的信息。在对所涉问题数据缺乏明确了解的情况下,我们证明单点观测可以独特地决定重量分布的支撑。证据的依据是测量的无症状行为以及分析的延续和Titchmarch变异理论。此外,当问题数据完全为人所知时,我们提供了现有结果的替代证据,其中指出,过多的一点边界观测可以独特地决定重量。提供了数项实验,以补充理论分析。