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

  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},
  • F. Mainardi
  • Published 1 May 2013
  • Mathematics
  • Discrete and Continuous Dynamical Systems-series B
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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