Analog implementation of fractional-order electric elements using caputo-fabrizio and atangana-baleanu definitions

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.