[405.1.2.1] In this section the composite fractional susceptibility
(of type

[405.1.3.1] Figure 1 shows a fit to the experimental data
of glycerol with the composite fractional
susceptibility function given in eq. (36).
[405.1.3.2] The upper figure displays the real part, the lower figure the
imaginary part of the frequency dependent susceptibility

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[405.1.3.7] Figure 1 shows that not only the asymmetric

[405.2.1.1] If an iterated composite fractional time evolution [page 406, §0] with four parameters is introduced an even better quantitative agreement can be obtained at all availaible temperatures. [406.1.0.1] In Figure 2 the composite fractional susceptibility

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with four parameters was used to fit the same data
as in Figure 1.
[406.1.0.2] This fit function has still two (resp. one) parameter less than
the conventional fit function of eq. (27).
[406.1.0.3] Note that in this case for

[406.1.1.1] The values of the fit parameters were found to depend sensitively on the frequency range that was included in the fit. [406.1.1.2] For this reason real and imaginary part were fitted separately. [406.1.1.3] The variation of the fit parameters for real and imaginary part gives an impression of the quality of the fit. [406.1.1.4] One source for parameter variations might be that the experimental data are patched together from differentmeasurements. [406.2.0.1] The matching of different data sets leads to visible breakpoints in the experimental data sets.

[406.2.1.1] In Figure 3 and 4
the fit parameters for real and imaginary parts
corresponding to the fits shown
in Figure 1 are plotted against temperature.
[406.2.1.2] Figure 4 shows the relaxation times in
an Arrhenius plot.
[406.2.1.3] Clear deviations from Arrhenius behaviour are found.
[406.2.1.4] Figure 3 shows the exponent

[407.1.1.1] In summary the present paper has derived a novel
three parameter susceptibility function from the
theory of fractional time evolutions [3].
[407.1.1.2] The new function contains only a
single stretching exponent.
[407.1.1.3] It shows two widespread characteristics of relaxation spectra
in glass forming materials: i) an asymmetry of
the