The complex interactions of aerodynamics, particularly the downwash effect associated with vertically configured vehicles, make stable flight challenging during the coordination of dense swarms of mini-quadcopter unmanned aerial vehicles (UAVs). Normal control approaches fail to consider the two-way dynamics among UAVs in a swarm; thus, these control approaches require a high safety margin. Thus, this paper presents a comparative study on the application of traditional proportional–integral–derivative (PID) and fractional-order PID (FOPID) control algorithms for the stabilization of dense UAV swarms. We propose a simplified six-degree-of-freedom dynamic model of quadcopter UAVs with a disturbance model of the downwash effects among aerial vehicles. The simulation results show that, compared with the traditional PID controller, the FOPID controller exhibits a 26.9% reduction in settling time, a reduced overshoot of 36.6%, and four-fold reduction in steady-state tracking error. In addition, the FOPID controller exhibits a better disturbance response because the time taken is 3.5 s shorter than that for the PID controller in a tight swarm configuration. These findings highlight the potential of the proposed FOPID controller for practical applications such as close-formation flight, swarm surveillance, and search-and-rescue missions, where safe and stable operation in dense UAV configurations is critical.