We present a study, within a mean-field theory, of the kinetics of the spin-1 Blume-Capel model on cylindrical Ising nanowire in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points. Then, we study the temperature dependence of the dynamic total magnetization to find the dynamic compensation points as well as to determine the type of behavior. We also investigate the effect of interaction parameters on the compensation phenomenon and construct the phase diagrams in four different planes. The system exhibits the compensation temperatures, or the N-, P-, Q-, S-type behaviors. Furthermore, we also observed two-compensation temperatures, namely W-type behaviors, whose result is compared with some experimental works and a good overall agreement is found.