Plenary Lecture

The Use of High Transcendental Functions in Mathematical Modelling

Professor Francesco Mainardi
Department of Physics
University of Bologna & INFN

Abstract: In Chapter 18, entitled “Miscellaneous Functions”, of the third volume of Bateman’s handbook (1950-1953) devoted to high transcendental functions, we find, in addition to the Mittag-Leffler and Wright functions (nowadays well known for their applications in fractional calculus and classified as Fox-H-functions) other functions including , the Volterra functions so named after the great Italian mathematician Vito Volterra (1860– 1940). In this lecture I would like to outline the main applications in mathematical modelling of all the so-called miscellaneous functions that are expected to exit from their state of Cinderella functions following the example of those of the Mittag-Leffler and Wright type. Furthermore we deal with other high transcendental functions that can be considered as variants of the classical Mittag-Leffler functions including those-introduced by Kilbas & Saigo.

Brief Biography of the Speaker: Presently Francesco MAINARDI is retired professor of Mathematical Physics from the University of Bologna (since November 2013) where he has taught this course since 40 years. Even if retired, he continues to carry out teaching and research activity. His fields of research concern several topics of applied mathematics, including diffusion and wave problems, asymptotic methods, integral transforms, special functions, fractional calculus and non-Gaussian stochastic processes.
At present his H-index is > 50.
For a full biography, list of references on author's papers and books see:
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