In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis.

翻译：本文研究了一维半扩散模型的反系数问题，该模型包含时间方向上的Caputo分数阶导数。反问题旨在利用一对空间侧边柯西数据确定两个系数及多个参数（分数阶阶数和区间长度）。此类柯西数据在时间上定义于非交叠集合，其中单一激励作用后，测量在激励支撑区域外的时间序列上完成。针对不同形式的侧边柯西数据，我们证明了两个唯一性定理。分析基于解的表达式、观测函数的解析性以及Sini [35]改进的逆Sturm-Liouville理论。研究结果充分依赖于分数阶扩散的记忆效应对模型中系数唯一恢复的关键作用。文中还给出若干数值实验以补充理论分析。