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* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
YouTube Channel: https://www.youtube.com/@FractionalCalculusSeminar
Mailing List (subscribe/unsubscribe) : https://lists.sissa.it/mailman/listinfo/fc-seminars
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.
- 09 August to 11 October 2024 : general fractional-calculus operators and fractional inverse problem
- 18 October to 06 December 2024 : Numerical analysis, methods and singular integral computation
List of Talks
## indicates two or more talks, scheduled on the same day.
$$ indicates talks at a different time, other than our usual time of 15:00 Rome
All times are quoted in local timezone of Rome, ITALY
Note : Summer time ends in ITALY on 27 October 2024, thus the clock shifts by one hour.
- 31 March to 27 Oct. 2024 : Central Eurpoean Summer Time (CEST)
- 27 Oct. onwards : Central Eurpoean Time (CET)
Best viewed in Desktop mode
Date (DD/MM/YYYY) |
Time (CET/CEST, Rome/Paris) |
Speaker |
Title |
25 / 01 / 2023 | 14:00-15:00 |
Arran Fernandez (Eastern Mediterranean University) |
Fractional differential equations: initialisation, singularity, and dimensions |
03 / 05 / 2024 |
14:30-15:30 |
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 |
14:30-15:30 |
Francesco Mainardi (University of Bologna and INFN) |
|
17 / 05 / 2024 | 14:30-15:30 |
Virginia Kiryakova (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences) |
|
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) |
|
07 / 06 / 2024 | 16:00-17:00## |
Eric J. Parish## (Sandia National Laboratory) |
|
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 |
15:00-16:00## |
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 |
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) |
|
09 / 08 / 2024 | 15:00-16:00 |
Anatoly N. Kochubei (Institute of Mathematics, National Academy of Sciences of Ukraine) |
Discrete-Time General Fractional Calculus |
16 / 08 / 2024 | 15:00-16:00 |
Vassili Kolokoltsov (University of Warwick, Coventry, United Kingdom) |
Rates of convergence of CTRWs to generalised fractional evolutions |
23 / 08 / 2024 | 15:00-16:00 |
Arran Fernandez (Eastern Mediterranean University, N. Cyprus) |
General kernels and parametrised families: in search of semigroup properties |
30 / 08 / 2024 | 15:00-16:00 |
Hafiz Muhammad Fahad (School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan) |
|
06 / 09 / 2024 | 15:00-16:00 |
Rudolf Hilfer (ICP, Universität Stuttgart, Allmandrng 3, 70569 Stuttgart, Germany) |
Fractional Calculus for Distributions |
13 / 09 / 2024 |
15:00-16:00 |
Karel Van Bockstal (Ghent University, Belgium) |
Inverse source problems for fractional diffusion equations |
20 / 09 / 2024 |
15:00-16:00 |
Ravshan Ashurov (Institute of Mathematics, Academy of Science of Uzbekistan) |
Inverse Problems of Determining the Order of Fractional Derivatives in Partial Derivative Equations |
27 / 09 / 2024 |
15:00-16:00 |
Jaan Janno (Tallinn University of Technology) |
A method to handle identification problems with unknown history and its application to determination of parameters of generalized fractional diffusion equations |
04 / 10 / 2024 | 15:00-16:00 |
Masahiro Yamamoto (The University of Tokyo) |
Uniqueness and stability results for inverse problems for time-fractional diffusion-wave equations |
11 / 10 / 2024 | 15:00-16:00 |
Barbara Kaltenbacher (University of Klagenfurt) |
Coefficient identification in a space-fractional equation with Abel type operators |
18 / 10 / 2024 |
16:00-17:00$$ |
Weihua Deng$$ (Lanzhou University, China) |
|
25 / 10 / 2024 |
16:00-17:00$$ |
Yue Yu$$ (Lehigh University) |
|
01 / 11 / 2024 |
13:00-14:00$$ |
Changpin LI$$ (Shanghai University)
|
|
08 / 11 / 2024 |
15:00-16:00 |
Lehel Banjai (Heriot-Watt University) |
Numerical methods for the spectral fractional Helmholtz equation |
15 / 11 / 2024 |
15:00-16:00## |
Erdogan Madenci## (University of Arizona, USA) |
|
15 / 11 / 2024 |
16:00-17:00## |
Roberto Garrappa## (University of Bari, Italy) |
|
22 / 11 / 2024 |
15:00-16:00## |
Zhongqiang Zhang## (Worcester Polytechnic Institute) |
Dealing with the singularity of fractional Laplacian with spectral methods |
22 / 11 / 2024 |
16:00-17:00## |
Pablo Seleson## (Oak Ridge National Laboratory) |
TBA |
29 / 11 / 2024 |
15:00-16:00 |
Christian Glusa (Sandia National Labs) |
Scalable methods for nonlocal models |
06 / 12 / 2024 |
15:00-16:00 |
Hong Wang (Department of Mathematics, University of South Carolina) |
Fractional PDEs for anomalous transport in porous media: model, analysis, discretization, and optimal control |
## indicates two or more talks, scheduled on the same day.
$$ indicates talks at a different time, other than our usual time of 15:00 Rome