  This paper is concerned with the inverse problem on determining an orbit of
the moving source in a fractional diffusion(-wave) equations in a connected
bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a
newly established fractional Duhamel's principle, we derive a Lipschitz
stability estimate in the case of a localized moving source by the observation
data at $d$ interior points. The uniqueness for the general non-localized
moving source is verified with additional data of more interior observations.
