Emeritus Professor
Francesco Mainardi
Department of Physics, University of Bologna, and INFN
Via Irnerio 46, I-40126 Bologna, Italy.
francesco.mainardi@bo.infn.it.it
fracalmo@gmail.com
The purpose of this course is to give an introduction on the main operators of Fractional Calculus (FC) and related Special Functions (SF) with some applications. The training programme consists in a basic course of 10 Lectures to be held in two weeks. Any lecture would be carried out in 2-3 academic hours including problem sessions.
Course Topics:
1. Functions of the Mittag-Leffler type
2. Riemann-Liouville Fractional Integrals and Derivatives
3. Regularized or Caputo Fractional Derivatives
4. Grünwald-Letnikov Fractional Derivatives
5. Riesz Fractional Integrals and Derivatives
6. Ordinary Fractional Differential Equations
7. Abel-Type Fractional Integral Equations
8. The Wright Functions: Fractional Diffusion Wave Equations
9. Applications in Linear Viscoelasticity
10. Application in Stochastic Processes
Basic Reference Books of the lecturer:
– F. Mainardi: Fractional Calculus and Waves in Linear Viscoelasticity, World Scientific, 2nd Edition 2022.
– R. Gorenflo, A.A Kilbas, F. Mainardi, S. Rogosin: Mittag-Leffler Functions: Theory and Applications, Springer Monographs in Mathematics, 2nd Edition 2020.
Brief Biography of the Speaker:
Presently Francesco MAINARD (Italian, born in 1942 is retired Professor of Mathematical Physics from the University of Bologna where has taught this course since more than 40 years. 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 > 70.
For a full biography, list of references on author’s papers and books see his CV (long version) and the Full List of Publications at December 2022 in the University of Bologna and Google Scholar.