We present a study, within a mean-field approach, of the kinetics of a classical mixed Ising ferrimagnetic model on a square lattice, in which the two interpenetrating square sublattices have spins σ = ±1/2 and S = ±1,0. The kinetics is described by a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external field and a crystal field interaction. We can identify two types of solutions: a symmetric one, where the total magnetization, M, oscillates around zero, and an antisymmetric one where M oscillates around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamical transition from one regime to the other can be of first or second order depending on the region in the phase diagram. Depending on the value of the crystal field we found up to two dynamical tricritical points where the transition changes from continuous to discontinuous. Also, we perform a similar study on the Blume-Capel (S = ±1,0) model and found strong differences between its behavior and the one of the mixed model. I
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