The nonequilibrium magnetic properties of a spin-1/2 cylindrical Ising nanowire system with core/shell in an oscillating magnetic field are studied by using a mean-field approach based on the Glauber-type stochastic dynamics (DMFT). We employ the Glauber-type stochastic dynamics to construct set of the coupled mean-field dynamic equations. First, we study the temperature dependence of the dynamic order parameters to characterize the nature of the phase transitions and to obtain the dynamic phase transition points. Then, we investigate the temperature dependence of the total magnetization to find the dynamic compensation points as well as to determine the type of behavior. The phase diagrams in which contain the paramagnetic, ferromagnetic, ferrimagnetic, partially nonmagnetic, surface fundamental phases and tree mixed phases as well as reentrant behavior are presented in the reduced magnetic field amplitude and reduced temperature plane. According to values of Hamiltonian parameters, the compensation temperatures, or the N-, Q-, P-, R-, S-type behaviors. Published by Elsevier Ltd.