  We present a study, within a mean-field approach, of the kinetics of a mixed
ferrimagnetic model on a square lattice in which two interpenetrating square
sublattices have spins that can take two values, $\sigma=\pm1/2$, alternated
with spins that can take the four values, $S=\pm3/2, \pm1/2$. We use the
Glauber-type stochastic dynamics to describe the time evolution of the system
with a crystal-field interaction in the presence of a time-dependent
oscillating external magnetic field. The nature (continuous and discontinuous)
of transition is characterized by studying the thermal behaviors of average
order parameters in a period. The dynamic phase transition points are obtained
and the phase diagrams are presented in the reduced magnetic field amplitude
$(h)$ and reduced temperature $(T)$ plane, and in the reduced temperature and
interaction parameter planes, namely in the $(h, T)$ and $(d, T)$ planes, $d$
is the reduced crystal-field interaction. The phase diagrams always exhibit a
tricritical point in $(h, T)$ plane, but do not exhibit in the $(d, T)$ plane
for low values of $h$. The dynamic multicritical point or dynamic critical end
point exist in the $(d, T)$ plane for low values of $h$. Moreover, phase
diagrams contain paramagnetic $(p)$, ferromagnetic $(f)$, ferrimagnetic $(i)$
phases, two coexistence or mixed phase regions, $(f+p)$ and $(i+p)$, that
strongly depend on interaction parameters.
