Seminar Uncertainty Quantification in Bayesian Clustering

Speaker: Garrit Page (Brigham Young University)

Abstract:

This talk addresses the problem of understanding whether solutions of fractional differential equations and systems remain stable over time, both for the widely used Caputo derivative and for the more general Prabhakar derivative. I will first revisit the classical Matignon result for systems of equations with Caputo derivatives, using an approach that highlights the role of certain kernel functions and the long-time behaviour of solutions. I will then turn to the more general setting of Prabhakar derivatives and show how the corresponding framework naturally extends the classical stability picture, with numerical examples illustrating transitions in dynamical behaviour. Finally, I will consider equations involving two separate Prabhakar terms, and I will present numerical results for an extended Duffing-type equation.

Organizer: Massimo Ventrucci