Analysis of excess wings in broadband
dielectric spectroscopy data of glass forming materials
provides evidence for anomalous time evolutions
and fractional semigroups.
Solutions of fractional
evolution equations in frequency space are used to
fit dielectric spectroscopy data of glass
forming materials with a range
between 4 and 10 decades in frequency.
It is shown that with only three parameters
(two relaxation times plus one exponent)
excellent fits can be obtained
for 5-methyl-2-hexanol and for
methyl-m-toluate over up to 7 decades.
The traditional Havriliak-Negami fit with three parameters
(two exponents and one relaxation time) fits only
Using a second exponent, as in Havriliak-Negami fits,
the -peak and the excess wing
can be modeled perfectly with our theory
for up to 10 decades
for all materials at all temperatures considered here.
Traditionally this can only be accomplished by combining
two Havriliak-Negami functions with 7 parameters.
The temperature dependent relaxation times are fitted with the
Vogel-Tammann-Fulcher relation which provides the corresponding
The relaxation times turn out to obey almost perfectly the
Computable expressions of time dependent
relaxation functions are also reported.