Fractional-Order in RC, RL and RLC Circuits

In mathematics, differential equations with fractional-order derivatives have a long history, for example, the “one in third” derivative, but haven’t gotten tremendous use in applied science and engineering. While applications do exist in several modeling specific phenomena, such as semi-infinite lossy transmission, which are difficult to model, and there exist some extensions of control in fractional-order PID, everyday use of fractional order modeling is more and more common. In this paper, the basic principles of the conventional RC and RL circuits in fractional-order way and a fractional differential equation are studied in the electrical RLC circuit. We consider the order of the derivative (0 u003c γ ≤ 1). In order to keep the dimensionality of the physical quantities R, L and C, an auxiliary parameter σ is introduced.