As fractional-order systems are becoming more widely accepted and their usage is increasing, it is important to understand their energy storage and loss properties. Fractional-order operators can be implemented using a distributed state representation, which has been shown to be equivalent to the Riemann–Liouville representation. In this paper, the distributed state for a fractional-order integrator is represented using an infinite resistor–capacitor network such that the energy storage and loss properties can be readily determined. This derivation is repeated for fractional-order derivatives using an infinite resistor–inductor network. An analytical example is included to verify the results for a half-order integrator. Approximation methods are included.

Issue Section:
Research Papers
Keywords:
Multi-scale dynamics
Topics:
Approximation, Energy storage, Impulse (Physics), Laplace transforms, Resistors, Capacitors, Circuits, Dynamics (Mechanics), Inductors

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