Speaker: Roberto Garrappa, Department of Mathematics / University of Bari, Italy

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

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

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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 differential equations, Variable order, Sonine-Scarpi kernels, Numerical methods

Abstract: Fractional differential equations of variable order have been introduced to more effectively capture system dynamics when the nature of memory effects is not constant.

Recently, a robust approach for extending constant-order fractional derivatives and integrals to variable order has been proposed [1]. Unlike traditional formulations, this approach relies on a generalization of classical operators in the Laplace transform domain rather than in the time domain. While mathematically consistent, it poses additional challenges for both theoretical analysis and numerical computation [3].

In this talk, we consider fractional differential equations whose order evolves according to a piecewise linear function, thus describing dynamics in which the order undergoes linear transitions triggered by specific events. The low regularity of the order function α(t) makes it impossible to apply most of the existing approaches (e.g., [2]) for computing the corresponding kernels in the time domain and solving the resulting equations.

After investigating the theoretical properties of the solutions, we discuss the main challenges arising in their numerical treatment and propose suitable numerical methods for their efficient solution.

Biography: Roberto Garrappa is Full Professor of Numerical Analysis at the University of Bari in Italy. His research focuses on numerical methods for fractional differential equations, special functions, and the development of efficient computational algorithms. He has made significant contributions to the computation of Mittag–Leffler, and to the numerical treatment of constant and variable order fractional differential equations. He has authored more than 70 scientific publications and several widely used MATLAB codes for fractional differential equations.

Bibliography

[1]  R.Garrappa, A.Giusti, F.Mainardi, ”Variable-order fractional calculus: A change of perspective”. In: Commun. Nonlinear Sci. Numer. Simul. (2021)
[2] R.Garrappa, A.Giusti. ”A computational approach to exponential-type variable-order fractional differential equations”. In: J. Sci. Comp. (2023)

[3] N.Al-Mutair, K.M.Furati, R.Garrappa. ”Variable-order Scarpi’s operators with approximated kernels”. Submitted (2026)
[4] R.Garrappa. ”Variable-Order fractional differential equations with piecewise-regular order transition”. In preparation