A unified modeling approach for characterization of fractional-order memory elements

A generalized mathematical model for current-controlled fractional-order memory elements is introduced in this work. The model characterizes constant-phase elements (CPEs) when its nonlinearity parameter is zero (k=0$$ k=0 $$); otherwise (k not equal 0$$ k\ne 0 $$), it characterizes three main types of fractional-order memory elements (memristor, meminductor, and memcapacitor). Time-domain analyses of the voltage and energy relations of the model are derived and verified via numerical and circuit simulations. Some new deductions on the effects of the respective fractional-order values are recorded: Each fractional-order element transposes into their corresponding resistive or memristive properties as their fractional-order values are varied; the meminductor's voltage response have undesired initial trails due to the fractional differentiator; the hysteresis loop of the meminductor is only pinched when its fractional-order values are unequal. A new CPE emulator circuit is designed, and a generalized memelement emulator is also designed and verified in PSpice circuit simulator: Circuit simulation results confirm the numerical analysis in all cases.