Abstract: In the last two decades there has been an increasing experimental and theoretical interest for relaxation processes fitting the prescription of the Mittag-Leffler (ML) function that establishes a bridge between stretched exponential and inverse power law decay. The ML function is also adopted by an increasing number of researchers to establish a new form of fractional derivative in time, currently applied to an impressively large number of processes, ranging from physics to neurophysiology. This talk is an attempt at explaining the universality origin of the ML survival probability as a form of central limit theorem closely related to the Levy-Gnedenko generalized central limit theorem. Conjectures are also made for the derivation of the ML function from a new form of renormalization group theory that may apply to all the complex systems, not necessarily physical systems, characterized by interaction between their units that promote global properties.
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