Paper:

# Analog Realization of Fractional-Order Capacitor and Inductor via the Caputo–Fabrizio Derivative

## Manjie Ran, Xiaozhong Liao^{†}, Da Lin, and Ruocen Yang

Automation Department, Beijing Institute of Technology

No.5 South Street, Zhongguancun, Haidian District, Beijing 100081, China

^{†}Corresponding author

Capacitors and inductors have been proven to exhibit fractional-order characteristics. Therefore, the establishment of fractional-order models for circuits containing such components is of great significance in practical circuit analysis. This study establishes the impedance models of fractional-order capacitors and inductors based on the Caputo–Fabrizio derivative and performs the analog realization of fractional-order electronic components. The mathematical models of fractional RC, RL, and RLC electrical circuits are deduced and verified via a comparison between the numerical simulation and the corresponding circuit simulation. The electrical characteristics of the fractional circuits are analyzed. This study not only enriches the models of fractional capacitors and inductors, but can also be applied to the description of circuit characteristics to obtain more accurate results.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.25 No.3, pp. 291-300, 2021.

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