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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]