Semi-active particle damping equipments exhibit considerable adaptability when implemented in flexible structures. However, their dynamic characteristics become complex due to the presence of a substantial quantity of particles within the damping equipment, and the influence of the internal magnetic field necessitates careful consideration. The fractional-order model of this kind of equipment is established, wherein the designed parameters kp and α are respectively associated with the filling ratio and the input current. Depending on the Hertz-Mindlin contact model, the multi-body dynamic issues inner the damping equipment are addressed using the Discrete Element Method, and then the fractional-order parameters kp and α are identified based on the energy distribution observed within a single vibration period. The numerical simulations, conducted using the fractional-order model, show a fundamental consistency with the experimental results. This alignment serves to validate the accuracy and feasibility of the fractional-order model. Finally, the fractional-order model is utilized to investigate the optimized value of the input current and to analyze the motion trajectory of the damping equipment under various scenarios. The results indicate that the optimized input current is approximately 2.5 A; and as the parameter kp and α increase, the motion trajectory of the system will rotate in a counterclockwise direction, accompanied by a gradual outward displacement of the outermost curve relative to the origin position.