Fractional Calculus Seminars

Fractional calculus is a generalised form of the integer-order calculus. While an integer-order derivative is a local operator, a fractional derivative is a non-local operator. The notion of Brownian motion is extended to admit Levy stable processes in the case of fractional diffusion. Many different operators have been described as fractional derivatives and integrals, with different properties and behaviours, and there are also further generalisations within non-local calculus. Real-world applications of non-local models can be found in turbulence, viscoelasticity, fracture mechanics, economics, electrical circuits, and plasma physics. Until recently, the theory and applications of fractional operators and equations did not receive much attention, so that many fundamental questions remain unanswered.

This seminar series is intended to provide deep knowledge on all aspects of fractional calculus, from analytical mathematics to numerical simulations to modelling applications. Starting in May 2024, we aim to have one talk every week, from a variety of experts in different topics related to fractional calculus.

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

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

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All times are quoted in local timezone of Rome, ITALY

Zoom meeting links will be public on respective talk's page - one hour before the talk.


Special focus sessions:

  • 24 May to 21 June 2024 : fractional/nonlocal modelling of turbulence.
  • 05 July to 02 August 2024 : stochastic processes / probability theory for fractional PDEs.

List of Talks

*** indicates two or more talks, scheduled on the same day.


Time (CET/CEST, Rome/Paris)



25 / 01 / 2023 14:00-15:00

Arran Fernandez

(Eastern Mediterranean University)

Fractional differential equations: initialisation, singularity, and dimensions

03 / 05 / 2024


Yuri Luchko 

(Berlin University of Applied Sciences and Technology)

The general Fractional Calculus operators with the Sonin kernels:  Basic properties, applications, and history of origins

10 / 05 / 2024


Francesco Mainardi

(University of Bologna and INFN)

An Introduction to Fractional Calculus

17 / 05 / 2024 14:30-15:30

Virginia Kiryakova

(Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

Classes of I- and bar-H- special functions related to Fractional Calculus and generalized fractional integrals

24 / 05 / 2024 14:30-15:30

Fujihiro Hamba

(Institute of Industrial Science,

University of Tokyo)

Analysis and Modeling of Non-local Eddy Diffusivity in Turbulent Flows

31 / 05 / 2024 15:00-16:00

Diego del-Castillo-Negrete

(Oak Ridge National Laboratory, USA)

Fractional diffusion models of nonlocal turbulent transport in plasmas and fluids

07 / 06 / 2024 15:00-16:00

Mohsen Zayernouri***

(Michigan State University)

Fractional-Order Large-Eddy Simulation of Turbulence

07 / 06 / 2024 16:00-17:00

Eric J. Parish***

(Sandia National Laboratory)

Subgrid-scale modeling with memory using the Mori-Zwanzig formalism and variational multiscale method

14 / 06 / 2024 15:00-16:00

Federico Nespoli

(Princeton Plasma Physics Laboratory)

Hyperdiffusion of dust particles in a turbulent tokamak plasma

21 / 06 / 2024


Daniel Boutros***

(University of Cambridge)

Phase transitions in the fractional three-dimensional Navier-Stokes equations

21 / 06 / 2024 16:00-17:00

Pavan Pranjivan Mehta***

(SISSA, International School of Advanced Studies, Italy)

Fractional Navier-Stokes Equations
28 / 06 / 2024 15:00-16:00

Kai Diethelm
(Technical University of Applied Sciences Wurzburg-Schweinfurt)

Efficient Algorithms for Computing Fractional Integrals
05 / 07 / 2024 15:00-16:00

Luisa Beghin

(Sapienza University, Rome)

Stochastic processes on infinite-dimensional spaces and fractional operators

12 / 07 / 2024 15:00-16:00

Enrico Scalas

(Sapienza University of Rome, Italy)

Fundamental solution of the space-time fractional diffusion equation using Monte Carlo simulations of CTRWs
19 / 07 / 2024 15:00-16:00

Ralf Metzler***

(Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany)

Fractional Brownian motion with time- and space-dependent Hurst exponent
19 / 07 / 2024 16:00-17:00

Mirko D'Ovidio***

(Dept. of Basic and Applied Sciences for Engeenering / Sapienza University of Rome)

26 / 07 / 2024 15:00-16:00

Michael Röckner

(Bielefeld University, Germany)

Nonlinear Fokker–Planck equations with fractional Laplacian and McKean–Vlasov SDEs with Lèvy–Noise
02 / 08 / 2024 15:00-16:00

Bruno Toaldo

(University of Turin)

Semi-Markov processes, time-changes and non-local equations

*** indicates two or more talks, scheduled on the same day.