  Analysis of excess wings in broadband dielectric spectroscopy data of glass
forming materials is found to provide 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. We show 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 4-5 decades. Using a second
exponent, as in Havriliak-Negami fits, the $\alpha$-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 6 parameters. The
temperature dependent relaxation times are fitted with the
Vogel-Tammann-Fulcher relation which provides the corresponding Vogel-Fulcher
temperatures. The relaxation times turn out to obey almost perfectly the
Vogel-Tammann-Fulcher law. Finally we report new and computable expressions of
time dependent relaxation functions corresponding to the frequency dependent
dielectric susceptibilities.
