  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.
