Discrete Cucker-Smale's flocking model with a weakly singular weight

For the discrete Cucker-Smale’s flocking model with a singular communication weight $\psi (s)=s^{-\alpha }$, with $0<\alpha <1\mathrm{/}2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result enables us to obtain existence and uniqeness of global solutions.