中文摘要：

基于分数阶微积分理论以及实际电容和实际电感在本质上是分数阶的事实，建立电感电流连续模式下Boost变换器的分数阶数学模型以及分数阶状态平均模型并进行理论分析，给出Boost变换器运行于电感电流连续模式下的参数条件．最后，基于Matlab／Simulink软件建立运行于电感电流连续模式下Boost变换器的分数阶仿真模型，并进行数值仿真分析以验证分数阶建模与理论分析的正确性．

英文摘要：

Based on fractional calculus and the fact that the capacitor and the inductor are fractional in nature, the fractional mathematical model and the fractional state averaged model of the Boost converter in continuous conduction mode operation are built and analyzed. Also, the condition for the continuous conduction mode operation of the Boost converter is given. Finally, in order to verify the theoretical analysis, the simulation model of the Boost converter in continuous conduction mode operation is established by using the software of Matlab/Simulink.