[123.6.1] The theory of fractional
dynamics yields a three parameter function,
that allows to fit both, the asymmetric peak and
the excess wing with a single stretching exponent
[17, 16, 23].
[123.6.2] The three parameter function is denoted as
“fractional dynamics” (FD) relaxation in
[123.6.3] Its functional form reads
is the binomial Mittag-Leffler function .
[123.6.4] The function from eq. (8)
solves the fractional differential equation
with , , and inital value
[123.6.5] In eq. (10)
the operator is the infinitesimal generator of
fractional time evolutions of index
[7, 11, 10, 9, 15, 23].
[123.6.6] It can be written as a fractional time derivative of
order in the form
where is the infinitesimal generator of translations.
[123.6.7] For a mathematical definition of see .
[123.6.8] Note, that the solution (8) of eq. (10)
holds also for generalized Riemann-Liouville operators
of order and type
as shown in [17, 16].
[123.6.9] The (right-/left-sided) generalized Riemann-Liouville fractional
derivative of order and type
with respect to was introduced in definition
3.3 in [15, p.113] by
denotes the right-sided
Riemann-Liouville fractional integral of order ,
and the left sided integral is defined analogously
Five different fits to the
imaginary part Im
of the complex dielectric function
of propylene carbonate at
as a function of frequency.
Experimental data represented by crosses are taken
from Ref. 
The range over which the data were fitted is indicated by
dashed vertical lines in the figure.
For clarity the data were displaced vertically by half a decade each.
The original location of the data corresponds to the curve