Speaker: Gianni Pagnini, BCAM--Basque Center for Applied Mathematics & Ikerbasque, Bilbao, Basque Country, Spain

Time : 15:00 - 16:00 CEST (Rome/Paris)

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

Zoom : A Zoom link will appear here, an hour before the talk

Organizers : 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

Keywords: Fractional theories and models, Rational-order fractional differential equations, Experimental corroboration

Abstract: Fractional differential equations are used in many fields for constructing new approaches that can fit data which  were not fitted yet through existing classical approaches based on integer-order derivatives. In this talk, we asked if fractional theories and models can be experimentally corroborated [1, 2]. This question lays on the experimental fact that parameter estimations have always a finite precision, and for this, they result always in rational numbers. When this observation is moved to fractional equations, then we have that fractional equations of rational orders admit solutions that solve also integer-order equations. Therefore, there exists a limitation to the corroboration of fractional theories and models. But, notwithstanding this corroboration failure, the fractional generalisation can be checked against a theoretical suitability criterion consisting in preserving mathematical and physical characteristics of the original problem, a criterion that is not met by the non-fractional generalisation [1]. This statement is first illustrated for the cases of fractional diffusion and fractional Schrodinger equation. Later the general case of a nonlinear fractional differential equation is analysed in detail.

Biography: Gianni Pagnini is permanent at BCAM - Basque Center for Applied Mathematics, Bilbao, Spain, as Ikerbasque Research Associate Professor, where he leads the Statistical Physics line. His scientific interests are stochastic processes and anomalous diffusion problems related with fractional differential equations. In particular, his research is intended for applications in biology and forest fires. He is active in the field of fractional calculus since his Laurea degree in Physics at the University of Bologna in 2000 under the supervision of Prof. F. Mainardi and Prof. R. Gorenflo. Currently, he is member of the Editorial Board of the journal "Fractional Calculus and Applied Analysis".

Bibliography

[1] Gianni Pagnini and Francesco Mainardi. “Are fractional theories and models experimentally corroborable?”. In: Foundations of Physics 55 (2025), 80.
[2] Davide Cusseddu. “Fractional derivatives in biomathematical models with memory: A critical discussion”. In: Journal of Mathematical Biology 92 (2026), 39.