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.

中文翻译：

---

使用 CAPUTO-FABRIZIO 和 ATANGANA-BALEANU 定义的分数阶电元件的模拟实现

本研究采用 Caputo-Fabrizio 和 Atangana-Baleanu 分数导数来确定分数电容器和电感器的阻抗和导纳模型。基于这两种导数，针对分数阶电气元件提出了模拟实现电路，可广泛应用于各种使用新分数算子的电气系统中。恒相电容和电感分别用Oustaloup算法和递归网栅型模拟电路近似。在此基础上，给出了Caputo-Fabrizio和Atangana-Baleanu定义下的分数电子元件的逼近电路。为了判断分数阶电容和电感的实现拓扑是否准确，取 Caputo 定义的分数阶 RC 和 RL 电路，以 Caputo-Fabrizio 和 Atangana-Baleanu 导数为例，进行了数值模拟和电路模拟的比较。验证了使用 Caputo-Fabrizio 和 Atangana-Baleanu 定义的模拟实现电路的正确性。以基于 Caputo、Caputo-Fabrizio 和 Atangana-Baleanu 导数的分数阶 RC 充电电路实验为例。进行了几个具有不同分数阶和电路参数的实验。实验数据进一步证明了实现方法的有效性。以基于 Caputo、Caputo-Fabrizio 和 Atangana-Baleanu 导数的分数阶 RC 充电电路实验为例。进行了几个具有不同分数阶和电路参数的实验。实验数据进一步证明了实现方法的有效性。以基于 Caputo、Caputo-Fabrizio 和 Atangana-Baleanu 导数的分数阶 RC 充电电路实验为例。进行了几个具有不同分数阶和电路参数的实验。实验数据进一步证明了实现方法的有效性。