<p>This paper investigates the existence and uniqueness of solutions, admissible Mittag-Leffler stability, and guaranteed cost synchronization for a class of fractional-order singular systems (FOSSs) with multiple time-varying delays. Using fixed-point theory, we establish sufficient conditions for the well-posedness of the system. To analyze stability, we propose a novel admissibility criterion that ensures the Mittag-Leffler stability of FOSSs while accounting for their singular nature. Building on this stability framework, we derive synchronization conditions for FOSSs with multiple time-varying delays and develop a guaranteed cost control strategy to enhance synchronization performance while minimizing control costs. Finally, three numerical examples, including a fractional-order electrical circuit system, are presented to validate the effectiveness of the proposed criteria and demonstrate their applicability to realistic engineering problems.</p>