1305.0161 (Francesco Mainardi)

On some properties of the Mittag-Leffler function E_α(-t^α),
completely monotone for t > 0 with 0 < α< 1    [PDF]

Francesco Mainardi

We analyse some peculiar properties of the function of the Mittag-Leffler (M-L) type, e_alpha(t):= E_alpha(-t^alpha) for 0 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.

View original: http://arxiv.org/abs/1305.0161