What is a fractional-order circuit?

Question

Despite some basic knowledge in electronics, and maybe because of my non-english tongue, I don't understand the term "fractional-order circuit", that I've read on a paper. Could a specialist explains the meaning of this term, as well as the applications of this field ?

That seems to be an emergent theme in EE (or resurgent) ?

Also Stability Analysis of Fractional-Order Circuits

@Andyaka I guess this is it? http://en.wikipedia.org/wiki/Fractional-order_system — travisbartley, Oct 03 '13 at 08:36
Yes. But, as I tried to explain, I'd like an explanation for curious people, especially about what it is used for. — JCLL, Oct 03 '13 at 11:28
@JCLL - I think you need to explain how you think it may be related to electrical engineering. — Andy aka, Oct 03 '13 at 12:32
I couldn't see anything that mentioned a fractional-order circuit - more help needed to understand your question. — Andy aka, Oct 03 '13 at 12:50

score 1 · Answer 1 · edited Jun 06 '22 at 18:03

Fractional-Order Circuit is applied Fractional-Calculus to Circuit Analysis

Commonly used for modeling bio-electrodes for cardiac tissue interfacing.
Offer more robustness than integer order control in PID controllers, using Fractional Integrators and Differetinators.

Not much knowledge in this field but heard something about Resistoductance, which is one component that incorporates fractional-order dynamics. It's a "linear electrical circuit element that posses the characteristics between an ohmic resistor and an inductor"

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Fractional Integrator and Differentiator Equations:

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score 1 · Accepted Answer · answered Oct 03 '13 at 15:15

'Nonlinear Noninteger Order Systems: Theory and Applications' by Paolo "Arena, R. Caponetto, M Porto, L. Fortuna, M." Porto (2001) Is a good book in this area.

Areas of applicability are: Non-inductive transmission lines, 1/f noise spectra, polarization effects in dielectrics, diffusion effects and a lot of acoustic effects. Some interesting control theory arises from the use of non-integer order control systems, the most well known is CRONE (french acronym for Command Robuste d'Ordre Non-Entier) - it provides for damping that is insensitive to the parameters of the system being controlled. There are even non linear \$PID\$ systems, of the form \$PI^\lambda D^\mu \$. Image processing with variable gamma is also a very common thing that people experience.

What is a fractional-order circuit?

2 Answers2