This paper investigates the influence of fractional dynamics on the Fisher information, concurrence and entropy squeezing of the SU(1,1) quantum system when interacting with both two- and three-level atoms, where the three-level atom is prepared in the \(\Lambda\) configuration. We analyze the dynamical behavior of these quantum systems using an effective fractional-time approach, exploring how the non-integer time-scaling parameter affects the quantum statistical properties. The study focuses on key measures such as the Fisher information, which provides insight into the precision of parameter estimation, and entropy squeezing, which characterizes the uncertainty and correlations between quantum states. In our analysis, we assume that the two-level atom is initially in the excited state, the three-level atom is in the upper state, and the field is prepared in the Perelomov coherent state. The fractional-time modeling is employed as a phenomenological tool to incorporate memory and non-Markovian effects beyond standard unitary dynamics. Our results demonstrate that the effective fractional parameter has a significant impact on these quantum information metrics, offering a deeper understanding of quantum systems in the presence of anomalous time evolution. These findings have implications for quantum control, quantum metrology, and the development of quantum technologies where non-Markovian dynamical effects play a role.
