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The Caputo–Fabrizio (C–F) definition, which solves the singularity problem in the Caputo definition, has been preliminarily applied in the field of circuit system modeling. However, the complex characteristics of the C–F definition-based circuit systems are still understudied. Therefore, this paper proposes a C–F definition-based fractional-order RLC (CF-FORLC) circuit model and analyzes its basic characteristics. First, the effects of different component orders on the performance parameters including the impedance, quality factor, and bandwidth are analyzed, which gives insights into the design of CF-FORLC. Then, the analytical solutions and the frequency-domain characteristics of CF-FORLC with different capacitance and inductance orders under arbitrary input are derived. Finally, the data of actual circuits are fitted to obtain the parameters of the CF-FORLC model, and the orders of the C–F definition-based capacitors and inductors are estimated. The results of the comparative experiments show that the proposed modeling scheme can improve the consistency of the dynamic performance of the model with that of the actual circuit. In addition, the proposed CF-FORLC model shows higher accuracy and flexibility with more adjustable parameters. [ABSTRACT FROM AUTHOR]

This study employs the Caputo–Fabrizio and Atangana–Baleanu fractional derivatives to determine the impedance and admittance model of fractional capacitor and inductor. The analog implementation circuits are proposed aiming at fractional-order electric elements based on these two derivatives, which can be widely used in a variety of electrical systems using new fractional operators. Constant phase capacitor and inductor are approximated by the Oustaloup algorithm and the recursive net-grid-type analog circuit, respectively. Based on that, approximation circuits of fractional electric components under Caputo–Fabrizio and Atangana–Baleanu definitions are given. For the purpose of judging whether the implementation topology of fractional-order capacitor and inductor is accurate, taking fractional RC and RL circuit defined by Caputo, Caputo–Fabrizio and Atangana–Baleanu derivatives as examples, the comparison of numerical and circuit simulations is carried out. The correctness of the analog implementation circuits using the Caputo–Fabrizio and Atangana–Baleanu definitions is verified. Fractional-order RC charging circuit experiments based on Caputo, Caputo–Fabrizio and Atangana–Baleanu derivatives are taken as examples. Several experiments with different fractional-order and circuit parameters are carried out. The validity of the implementation methods is ulteriorly proved with experiment data. [ABSTRACT FROM AUTHOR]