# On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$

@article{Mainardi2013OnSP, title={On some properties of the Mittag-Leffler function \$\mathbf\{E\_\alpha(-t^\alpha)\}\$, completely monotone for \$\mathbf\{t> 0\}\$ with \$\mathbf\{0<\alpha<1\}\$}, author={Francesco Mainardi}, journal={Discrete and Continuous Dynamical Systems-series B}, year={2013}, volume={19}, pages={2267-2278} }

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 (surprisingly) these two spectra coincide so providing
a universal scaling property of this function, not well pointed out in the literature.
Furthermore, we consider the problem of…

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