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Nonequilibrium phase transition properties of a mixed Ising ferrimagnetic model consisting of spin-1/2 and spin-3/2 on a square lattice under the existence of a time dependent oscillating magnetic field have been investigated by making use of Monte Carlo simulations with a single-spin flip Metropolis algorithm. A complete picture of dynamic phase boundary and magnetization profiles have been illustrated and the conditions of a dynamic compensation behavior have been discussed in detail. According to our simulation results, the considered system does not point out a dynamic compensation behavior, when it only includes the nearest-neighbor interaction, single-ion anisotropy and an oscillating magnetic field source. As the next-nearest-neighbor interaction between the spins-1/2 takes into account and exceeds a characteristic value which sensitively depends upon values of single-ion anisotropy and only of amplitude of external magnetic field, a dynamic compensation behavior occurs in the system. Finally, it is reported that it has not been found any evidence of dynamically first-order phase transition between dynamically ordered and disordered phases, which conflicts with the recently published molecular field investigation, for a wide range of selected system parameters. [ABSTRACT FROM AUTHOR]