In this study an effective method is introduced to stabilize fractional-order descriptor time-delay systems, while time-delay can belong to a specified interval from zero to a given amount of delay. A novel approach to decompose fractional-order descriptor time-delay systems (FODTDSs) and transform them to normal fractional-order time-delay systems (FOTDSs) with a lower order is presented. Also, as this decomposition reduces the order of the system, reducing the computational complexity is one of the important benefits of this method. By presenting two examples in this paper, the applicability and effectiveness of this method are shown.