Date:
Speaker : Roberto Garrappa, University of Bari, Italy
Time : 16:00 - 17:00 CET (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom : A link will appear here
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 derivatives, variable order, Laplace transform
Abstract:A new and different approach to generalize fractional-order operators from constant to variable order has been recently proposed and investigated [1]. The new variable-order operators find inspirations on some pioneering works by the Italian engineer Giambattista Scarpi and dating back to the early seventies [2]. The main difference with other variable-order operators is that the generalization from constant to variable order is made in the Laplace transform domain rather than directly in the time domain, with an important advantage: based on the Sonine condition, once the integral operator has been defined, the construction of the corresponding differential operator, ensuring inversion of the integral, is straightforward.
The numerical treatment of fractional differential equations with this family of variable-order operators is not trivial and requires methods constructed to operate in the Laplace transform domain. In this talk, we first review the main mathematical aspect of the proposed operators, we briefly discuss some applications [3,4], and hence we treat with more details some numerical aspects related to solving variable-order fractional differential equations [5].
Biography: Roberto Garrappa is a full professor of Numerical Analysis at the University of Bari. His main research interest focuses on the numerical solution of differential equations of fractional order and on the analysis and numerical evaluation of special functions. He is author of more than 70 scientific papers and of a series of Matlab codes for fractional-order problems freely available on the Mathworks website.
Bibliography
[1] R.Garrappa, A.Giusti, F.Mainardi, Variable-order fractional calculus: a change of perspective, Communications in Nonlinear Science and Numerical Simulation, 2021, 102, 105904
[2] G. Scarpi, Sopra il moto laminare di liquidi a viscosistà variabile nel tempo. Atti Accademia delle Scienze, Isitituto di Bologna, Rendiconti (Ser. XII) 9, 54–68 (1972)
[3] L.Beghin, L.Cristofaro, R.Garrappa Renewal processes linked to fractional relaxation equations with variable order Journal of Mathematical Analysis and Applications, 2024, 531(1), Art. no. 127795
[4] A.Giusti, I.Colombaro, R.Garra, R. Garrappa, A.Mentrelli. On variable-order fractional linear viscoelasticity. Fractional Calculus and Applied Analysis, 2024, 27, 1564-1578
[5] R.Garrappa, A.Giusti, A computational approach to exponential-type variable-order fractional differential equations, Journal of Scientific Computing, 2023, 96, Art. no. 63
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