<p>This study investigates the bifurcation and chaotic phenomena in the nonlinear dynamics of a giant magnetostrictive actuator (GMA) under fractional-order delayed feedback control. Firstly, the concepts of equivalent stiffness and equivalent damping were introduced to approximate the fractional-order delayed feedback control term. Secondly, the Melnikov method was employed to derive the threshold condition for the controlled GMA system to enter Smale horseshoe chaos, and the accuracy of the analytical solution was verified via numerical simulations. Finally, the effects of the excitation frequency, damping coefficient and control parameters on the chaotic threshold of the system were explored via numerical simulations, with feasible regions identified to avoid chaotic motion in the GMA system. The results demonstrate that the proposed control method effectively eliminates bifurcation and chaos in GMA system dynamics. After the control parameters were adjusted, the regions of periodic and aperiodic motions in the system could be modified. These findings provide valuable insights into chaos suppression in similar systems.</p>