Inverse moving source problem for time-fractional evolution equations: determination of profiles

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations a derivative order $\alpha\in(0,2]$ time. In the first problem, sources are supposed to move along known straight lines, and we suitably choose partial interior observation data finite Reducing determination of initial values, prove unique one profiles for $0<\alpha\le1$ $1<\alpha\le2$, respectively. second orbits assumed be known, consider full lateral Cauchy data. At cost infinite time, by constructing test functions.