**Plenary Lecture
Fractional Calculus and Special Functions in Applied Mathematics**

**Professor Francesco Mainardi**

Department of Physics

University of Bologna & INFN

ITALY

E-mail: francesco.mainardi@bo.infn.it

**Abstract: ** Fractional calculus, in allowing integrals and derivatives of any positive real order (the term "fractional" is kept only for historical reasons), can be considered a branch of mathematical physics which deals with integro-differential equations where the integrals are of convolution type and exhibit (weakly singular) kernels of power-law type. As a matter of fact fractional calculus and special functions with the use of integral transforms allow us to deal a number of problems in the fields of applied mathematics (from rheology to diffusion and wave propagation). In this plenary lecture we discuss some interesting problems in order to single out the efficiency of these tools.

Basic References of the Speaker:

- Mainardi, F. (2010): Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, London and World Scientific, Singapore. 2nd edition in preparation.

- Gorenflo, R., Kilbas, A., Mainardi, F. and Rogosin, S. (2014): Mittag-Leffler Functions, Related Topics and Applications, Springer Verlag, Berlin. 2nd edition in preparation

**Brief Biography of the Speaker: ** Presently Francesco MAINARDI (PhD in Theoretical Physics) is retired professor of Mathematical Physics from the University of Bologna (since November 2013) where he has taught this course since more than 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 fractional calculus, special function, diffusion and wave problems, asymptotic methods, integral transforms, rheology , non-Gaussian stochastic processes, At present his H-index is > 60. For a full biography, list of references on author's papers and books see: Home Page: http://www.fracalmo.org/mainardi/index.htm Profile: http://scholar.google.com/scholar?hl=en&lr=&q=f+mainardi