  Power laws in time and frequency appear in fields such as linear
viscoelasticity and acoustics, viscous boundary layer problems, and
dielectrics. This is consistent with fractional derivatives in the fundamental
descriptions, since power laws in time and frequency are related by the Fourier
transform, and also associated with fractional derivatives. Examples here
include power-law frequency dependent attenuation in ultrasound, elastography
and sediment acoustics. In viscous boundary problems there is a viscodynamic
operator in the Biot poroviscoelastic theory which may be formulated with a
fractional derivative. Power law and stretched exponential temporal responses
of non-ideal capacitors can also be shown to relate to the Cole-Cole power-law
dielectric model.

General Physics