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.
Organisers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
SISSA Liasion : Gianluigi Rozza* (grozza@sissa.it)
* 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
Official Website for 2024 : https://mathlab.sissa.it/fractional-calculus-seminars
Official Website for 2025 : https://mathlab.sissa.it/fractional-calculus-seminars-2025
Contents (Talks topic-wise listed)
(1) Arran Fernandez : Fractional differential equations:initialisation, singularity, and dimensions
(3) Francesco Mainardi : An Introduction to Fractional Calculus
(5) Anatoly N. Kochubei : Discrete-Time General Fractional Calculus
(6) Arran Fernandez : General kernels and parametrised families: in search of semigroup properties
(8) Rudolf Hilfer : Fractional Calculus for Distributions
(10) Zivorad Tomovski : Some analytical inequalities in fractional calculus
(13) Tibor K. Pogany : On use of Grunwald–Letnikov fractional derivative in analysis
(15) Oleg Marichev : Integral transforms with Fox H-functions in kernels
(1) Vassili Kolokoltsov : Rates of convergence of CTRWs to generalised fractional evolutions
(2) Bruno Toaldo : Semi-Markov processes, time-changes and non-local equations
(4) Mirko D’Ovidio : Fractional Boundary Value Problems: Results and Applications
(5) Ralf Metzler : Fractional Brownian motion with time- and space-dependent Hurst exponent
(7) Luisa Beghin : Stochastic processes on infinite-dimensional spaces and fractional operators