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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 \star-product, a generalization of the Volterra convolution, followed by an appropriate discretization of the resulting expression. Additionally, we demonstrate that, in certain cases, the \star-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