We present a study, within a mean-field approach, of the stationary states of the kinetic spin-3/2 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization (m) of the system oscillates in time around zero, which corresponds to a paramagnetic phase (P), and an antisymmetric one where m oscillates in time around a finite value different from zero, namely +/- 3/2 and +/- 1/2 that corresponds to the ferromagnetic-3/2 (F-3/2) and the ferromagnetic-1/2 (F-1/2) phases, respectively. There are coexistence regions of the phase space where the F-3/2, F-1/2 (F-3/2+F-1/2), F-3/2, P (F-3/2+P), F-1/2, P (F-1/2+P), and F-3/2, F-1/2, P (F-3/2+F-1/2+P) phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.