Achieving a simplified model is a major issue in the field of fractional-order nonlinear systems, especially large-scale systems. So that in addition to simplifying the model, the outstanding features of the fractional-order modeling, such as memory feature, are preserved. This paper presented the homotopy singular perturbation method (HSPM) to reduce the complexity of the model and use the advantages of both models of the fractional order and the integer order. This method is a combination of the fractional-order singular perturbation method (FOSPM) and the homotopy perturbation method (HPM). Firstly, the FOSPM is developed for fractional-order nonlinear systems; then, a modification of the HPM is proposed. Finally, the HSPM is presented using a combination of these two methods. fractional-order nonlinear systems can be divided into two lower-order subsystems such as nonlinear or linear integer-order subsystem and linear fractional-order subsystem using this hybrid method. Convergence analysis of tracking error to zero is theoretically presented, and the effectiveness of the proposed method is also evaluated with two examples. Next, the number and location of equilibrium points are compared between the original system and the subsystems obtained from the proposed method. In the end, we show that the stability of fractional-order nonlinear system can be determined by investigating the stability of the subsystems using Theorem 3 and Lemma 2.

实现简化模型是分数阶非线性系统（尤其是大规模系统）领域的主要问题。这样，除了简化模型外，还保留了分数阶建模的突出功能，例如内存功能。本文提出了同伦奇异摄动法（HSPM），以降低模型的复杂性并利用分数阶和整数阶这两种模型的优势。此方法是分数阶奇异摄动法（FOSPM）和同伦扰动法（HPM）的组合。首先，FOSPM是为分数阶非线性系统开发的。然后，提出了对HPM的修改。最后，结合使用这两种方法来介绍HSPM。使用这种混合方法，分数阶非线性系统可以分为两个低阶子系统，例如非线性或线性整数阶子系统和线性分数阶子系统。从理论上介绍了跟踪误差为零的收敛性分析，并通过两个例子对所提方法的有效性进行了评估。接下来，比较原始系统和从所提出的方法获得的子系统之间的平衡点的数量和位置。最后，我们表明分数阶非线性系统的稳定性可以通过使用定理3和引理2研究子系统的稳定性来确定。从理论上介绍了跟踪误差为零的收敛性分析，并通过两个例子对所提方法的有效性进行了评估。接下来，比较原始系统和从该方法获得的子系统之间平衡点的数量和位置。最后，我们表明分数阶非线性系统的稳定性可以通过使用定理3和引理2研究子系统的稳定性来确定。从理论上介绍了跟踪误差为零的收敛性分析，并通过两个例子对所提方法的有效性进行了评估。接下来，比较原始系统和从所提出的方法获得的子系统之间的平衡点的数量和位置。最后，我们表明分数阶非线性系统的稳定性可以通过使用定理3和引理2研究子系统的稳定性来确定。