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<p>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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\star \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>⋆</mo> </math></EquationSource> </InlineEquation>-product, a generalization of the Volterra convolution, followed by an appropriate discretization of the resulting expression. Additionally, we demonstrate that, in certain cases, the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\star \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>⋆</mo> </math></EquationSource> </InlineEquation>-formalism enables the derivation of closed-form solutions, further highlighting the utility of this framework.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Fabio Durastante,
  • Pierre-Louis Giscard,
  • Stefano Pozza

摘要

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.