<p>This study investigates the application of multi-strategy time-delayed feedback control for suppressing primary resonance in fractional horizontal roller systems. Departing from existing research, which primarily focuses on single displacement feedback, we systematically analyze three nonlinear time-delayed feedback strategies, namely displacement, velocity, and acceleration feedback. We also propose a velocity-displacement hybrid feedback control strategy to address the limitations of single strategies. Subsequently, the multiple scale method is employed to derive the amplitude-frequency response equations of the primary resonance under each control strategy. Numerical simulations, including time history and phase diagram analyses, demonstrate that the proposed time-delayed controllers effectively eliminate nonlinear jumping and hysteresis phenomena, and induce a transition from chaotic to periodic motion in the system. Comparative analysis shows that velocity feedback performs best among single strategies while the velocity-displacement hybrid strategy achieves balanced control across a broader range. The results enhance theoretical understanding of fractional-order nonlinear dynamics in rolling systems and offer practical guidance for vibration reduction in horizontal roller systems.</p>