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

[2507.16652] A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2507.16652 (math) [Submitted on 22 Jul 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations Authors: Fabio Durastante , Pierre-Louis Giscard , Stefano Pozza View a PDF of the paper titled A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations, by Fabio Durastante and 2 other authors View PDF 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. Comments: 33 pages, 6 tables, 7 figures Subjects: Numerical Analysis (math.NA) MSC classes: 26A33, 65L05, 33C45 Cite as: arXiv:2507.16652 [math.NA] (or arXiv:2507.16652v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2507.16652 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Fract Calc Appl Anal (2026) Related DOI : https://doi.org/10.1007/s13540-026-00529-2 Focus to learn more DOI(s) linking to related resources Submission history From: Fabio Durastante Dr. [ view email ] [v1] Tue, 22 Jul 2025 14:49:17 UTC (624 KB) [v2] Sat, 11 Apr 2026 12:02:59 UTC (1,079 KB) Full-text links: Access Paper: View a PDF of the paper titled A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations, by Fabio Durastante and 2 other authors View PDF TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-07 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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