A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations
Numerical Analysis
2026-05-08 v2 Numerical Analysis
Abstract
This article presents a novel solution method for nonautonomous linear ordinary fractional differential equations. The approach is based on reformulating the analytical solution using the -product, a generalization of the Volterra convolution, followed by an appropriate discretization of the resulting expression. Additionally, we demonstrate that, in certain cases, the -formalism enables the derivation of closed-form solutions, further highlighting the utility of this framework.
Keywords
Cite
@article{arxiv.2507.16652,
title = {A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations},
author = {Fabio Durastante and Pierre-Louis Giscard and Stefano Pozza},
journal= {arXiv preprint arXiv:2507.16652},
year = {2026}
}
Comments
33 pages, 6 tables, 7 figures