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arXiv · 2507.16652

A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations

Fabio Durastante·Pierre-Louis Giscard·Stefano Pozza
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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.

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Fabio Durastante, Pierre-Louis Giscard, Stefano Pozza. 2025-07-22. A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations. https://doi.org/10.1007/s13540-026-00529-2

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