Through the generalized fractional derivative, it is studied how the decay term and the fractional parameter affect the quantum system, specifically the interaction between the SU(1,1) algebraic system and a three-level atom. By transforming the differential equations into fractional differential equations, general fractional solutions are obtained. The influence of decay and fractional parameter on phenomena such as revival and collapse, entropy squeezing, purity, and concurrence are investigated. The results demonstrate how both decay and fractal parameter affect periods of collapse and revival. It is worth noting that the decay parameter shortens the collapse periods, while an increase in the fractional parameter leads to longer collapse periods. The decay parameter also reduces the degree of entanglement between the different components of the quantum system, while increasing the fractional parameter enhances the entanglement within the quantum system. Hence, it can be concluded that the fractional parameter plays a crucial role in the observed effects on the studied properties.