Time and frequency responses of non-integer order RLC circuits

By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be 0 < gamma <= 1. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.