Speaker: Eva Kaslik, West University of Timisoara, Romania

Time : 15:00 - 16.00 CEST (Rome/Paris)

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

YouTube : https://youtu.be/8CxF-1IB8fw

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: Prabhakar derivative; fractional-order systems; stability

Abstract: The Prabhakar function E^γ_α,β (z) and the corresponding kernel e^γ_α,β,ω(t) = t^β−1 E^γ_α,β (ωt^α) provide a unifying framework for stability analysis and computation in fractional-order systems [1, 2, 3].

I will begin with a kernel-based proof of a slight refinement of Matignon’s theorem for commensurate Caputo systems [4], highlighting the role of the Prabhakar kernel and its large-time asymptotic properties.

Moving beyond Caputo derivatives, I will then treat linear systems with Caputo-Prabhakar derivatives [5]. Here the characteristic equation s^β−αγ (s^α − ω)^γ = λ induces a
root-locus boundary Ψ^γ_α,β,ω and a stability region S^γ_α,β,ω that reduces to Matignon’s wedge when γ → 0. I will also show asymptotic expansions for small/large times and numerical illustrations, including a Hopf-type transition in a Brusselator model as ω varies.

The final part of the talk refers to the stability analysis of two-term Prabhakar FDEs. As an illustrative example, an extension of the Duffing equation is numerically investigated, developing an implicit L1/L2-type scheme adapted to Prabhakar kernels

Biography: Eva Kaslik is a Full Professor at the Department of Computer Science of the West University of Timisoara, Romania. She earned her PhD in Applied Mathematics in 2006 at  Université Sorbonne Paris Nord (Paris 13), through a joint degree program with the West University of Timisoara. She obtained her Habilitation in Mathematics in 2015. She has authored or co-authored over 100 peer-reviewed publications and serves as a member of the Editorial Board of several journals, including "Fractional Calculus and Applied Analysis" and "Mathematics and Computers in Simulation". Her main research focuses on stability theory for fractional-order and delay differential systems, and mathematical modeling in the neurosciences. She also advises graduate students and collaborates widely across applied mathematics, dynamical systems, and computational science.

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