  We analyse some peculiar properties of the function of the Mittag-Leffler
(M-L) type, $e_\alpha(t):= E_\alpha(-t^\alpha)$ for $0 <\alpha < 1$ and $t >
0$, which is known to be completely monotone (CM) with a non negative spectrum
of frequencies and times, suitable to model fractional relaxation processes. We
first note that these two spectra coincide so providing a universal scaling
property of this function. Furthermore, we consider the problem of
approximating our M-L function with simpler CM functions for small and large
times. We provide two different sets of elementary CM functions that are
asymptotically equivalent to $e_\alpha(t)$ as $t \to 0$ and $t \to \infty$.
