An Introduction to Fractional Calculus


Friday, 10 May, 2024 - 14:30 to 15:30

Speaker : Francesco Mainardi, University of Bologna and INFN, Italy

Time : 14:30 - 15.30 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

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Organizers : Pavan Pranjivan Mehta* ( and Arran Fernandez** (

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Fractional calculus, Mittag-Leffler functions, Wright functions

Abstract: We introduce the linear operators of fractional integration and fractional differentiation in the framework of the so called fractional calculus (FC). Our approach is essentially based on an integral formulation of fractional calculus acting on sufficiently well behaved functions defined in R that include the Riemann-Liouville, Caputo and Riesz-Feller approaches with the related special functions. The list of applications of FC is huge and includes, just to cite a few, Visco-elasticity, Electrical Circuits, Control theory, intermediate phenomena between Diffusion and Wave propagation, Biology, Bioengineering, Image processing, Finance, Stochastic processes

Biography: 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 research activity. His fields of research concern several topics of applied mathematics, including linear viscoelasticity, 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: 

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[1] R. Gorenflo, A.A Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions. Related Topics and Applications, Springer, Berlin (2020), Second Edition.

[2] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelastity, World Scientific, Singapore (2022), Second Edition.