The Pioneers of the Mittag-Leffler Functions in Dielectrical and Mechanical Relaxation Processes
Francesco Mainardi, Armando Consiglio
TL;DR
This paper reviews the fundamental properties of Mittag-Leffler functions and highlights their crucial role in modeling relaxation phenomena in dielectrics and viscoelastic materials, building on historical insights from pioneers Davis and Gross.
Contribution
It provides a concise survey of Mittag-Leffler functions and emphasizes their application in explaining relaxation processes, connecting historical developments with modern understanding.
Findings
Mittag-Leffler functions effectively model relaxation phenomena.
Historical analysis links pioneers' work to current applications.
The functions explain after-effects in dielectrics and viscoelastic bodies.
Abstract
We start with a short survey of the basic properties of the Mittag-Leffler functions. Then we focus on the key role of these functions to explain the after-effects and relaxation phenomena occurring in dielectrics and in viscoelastic bodies. For this purpose we recall the main aspects that were formerly discussed by two pioneers in the years 1930's-1940's whom we have identified with Harold T. Davis and Bernhard Gross.
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