Comparative Study of Riemann–Liouville and Caputo Derivative Definitions in Time-Domain Analysis of Fractional-Order Capacitor

The fractional-order capacitor applied in power electronic converters, filters or other circuits has become a hot spot due to benefits, such as high-performance and flexibility. Two typical kinds of fractional-order derivative definitions, Riemann-Liouville (RL) or Caputo derivatives are popularly used to analyze the characteristics of fractional-order capacitor. However, it remains a fundamental challenge to find that when and which fractional-order derivative definition is more suitable in the time-domain analysis of fractional-order capacitor. In this brief, comparative investigations about the transient and steady analysis of a fractional-order capacitor adopting these two definitions are performed. It is determined that difference comes from description of dynamic process. In particular, the difference is especially obvious for the cases of step-up input. Based on the analysis, this brief proposed that RL derivative is a more accurate choice for modeling and analyzing fractional-order capacitor in time domain. Moreover, RL derivative is also more suitable for solving fractional-order circuits with fractional-order capacitor. The results from simulations and experiments verify the conclusion.