A new closed-form expression for the solution of ODEs in a ring of distributions and its connection with the matrix algebra

2023/02/22 by Stefano Pozza, Pozza, Stefano · 2 citations
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2302.11375

openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix. This is done by studying a particular subring and connecting it with a subalgebra of infinite matrices.

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• A ⋆-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations

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