文中建立了电感电流连续模式（CCM）运行的分数阶Cuk变换器的非线性等效电路模型和非线性数学模型，利用等效小参量（ESP）符号分析法得到了其等效数学模型；然后基于谐波平衡原理，迭代求解获得了变换器状态变量瞬态和稳态近似周期解；进而分析了电感和电容分数阶次对状态变量直流工作点和周期解闭合轨道以及纹波分量的影响，并通过仿真验证了文中方法所得状态变量瞬态解和稳态解的准确性；最后，以电感和电容阶次均为0.9的分数阶Cuk变换器为例进行了实验验证。实验和文中方法所得状态变量（输出电压与电感电流）的稳定时间分别为1.56 ms和1.52 ms，输出电压平均值分别为2.110 V和2.959 V，纹波电压峰值分别为96 mV和109 mV，电感电流平均值分别为0.112 A和0.148 A，纹波电流峰值分别为52 mA和59 mA。可见，对于状态变量的瞬态和稳态特性，文中方法和实验所得结果均比较接近。文中还进一步验证了该方法的有效性以及所得状态变量瞬态和稳态解的准确性。文中方法所得分数阶变换器的稳态解同储能元件的阶次相关，可用于分析分数阶阶次对电路特性的影响；此外，也可根据所得到的稳态解的解析表达式，对变换器系统的稳定性进行分析。

This paper established the nonlinear equivalent circuit model and nonlinear mathematical model of the fractional-order Cuk converter operating in Continuous Conduction Mode (CCM), and obtained the equivalent mathematical model by using the equivalent small parameter (ESP) symbolic analysis method. Then, based on the principle of harmonic balance, it iteratively obtained the transient and steady-state approximate periodic solutions of the transients and steady-state variables of the transformer state variables. Furthermore, it analyzed the influence of fractional inductance and capacitance on the DC operating point and periodic declosing orbit and ripple component of the state variable, and the accuracy of the transient solution and steady-state solution of the state variable obtained by the proposed method was verified by simulation. Finally, an experimental verification was carried out on a fractional-order Cuk converter with an inductor and capacitor order of 0.9. The settling times of the state variables (output voltage and inductor current) obtained by the experiment and the method are 1.56 ms and 1.52 ms, the average output voltage is 2.110 V and 2.959 V, the peak ripple voltage is 96 mV and 109 mV, the average inductor current is 0.112 A and 0.148 A, and the peak ripple current is 52 mA and 59 mA, respectively. It can be seen that for the transient and steady-state characteristics of state variables, the results obtained in the method and experiments are relatively close. The study further verified the effectiveness of the method and the accuracy of the transient and steady-state solutions of the obtained state variables. The steady-state period solution of the fractional-order converter obtained in this method is related to the order of the fractional energy storage element, so it can be used to analyze the influence of fractional-order on circuit characteristics. In addition, the stability of the converter system can also be analyzed according to obtained analytical expression of obtained steady-state solution.