<p>Previous fractional-order gene regulatory network models predominantly considered discrete delays, which may not fully capture the continuous nature of delay or the more complex combinations of multiple delays in realistic gene expression scenarios. To address this issue, this paper presents a fractional-order gene regulatory network model with mixed delays, including both discrete and distributed delays, and investigates the stability and synchronization properties of the system. Specifically, a sufficient condition for global Mittag-Leffler stability is derived by combining the Lyapunov-Razumikhin method with fractional-order calculus. Furthermore, an adaptive control strategy is proposed to achieve finite-time synchronization, and key criteria for effective control are established. Finally, numerical simulations are provided to validate the effectiveness and advantages of the proposed control strategy in handling mixed delays.</p>