arXiv subjects

Lucas Venturato

Publications and source records attributed to Lucas Venturato.

4 recordsLinked to original sources

arXiv2026

Learning from user's behaviour of some well-known congested traffic networks

The traffic assignment problem (TAP) aims to predict how traffic flows distribute themselves across a road network, traditionally requiring computationally expensive iterative simulations to reach a user equilibrium (UE) where no driver can unilaterally reduce their travel time. Recent developments in machine learning (ML), particularly Graph Neural Networks (GNNs) and hybrid approaches, aim to solve this faster while maintaining accuracy

math.OC↗

arXiv2021

A one-phase space -- fractional Stefan problem with no liquid initial domain

Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for a one dimensional material with a non-local flux, expressed in terms of the Caputo derivative, which derives in a space-fractional Stefan problem. We prove existence of a unique solution to a phase-change problem with the fractional Neumann boundary condition at the fixed face $x=0$, where the domain, at the initial time, consists of liquid and solid. Then we use this result to prove the existence of a limit solution to an analogous problem with solid initial domain, when it is not possible to transform the domain into a cylinder.

math.AP↗

arXiv2020

About Convergence and Order of Convergence of some Fractional Derivatives

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.

math.AP↗

arXiv2018

Global Solution to a Nonlinear Fractional Differential Equation for the Caputo-Fabrizio Derivative

This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the fractional Integral of Caputo--Fabrizio is also analyzed. The main result consists in the proof of existence and uniqueness of a global solution to a nonlinear fractional differential equation, which has been solved previously for short times by Lozada and Nieto (Progr. Fract. Differ. Appl., 1(2):87--92, 2015). The effects of memory as well as the convergence of the obtained results when $\al \nearrow 1$ (and the classical first derivative is recovered) are analyzed throughout the paper.

math.AP↗