A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910194929238016 |
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| author | Durastante, Fabio Giscard, Pierre-Louis Pozza, Stefano |
| author_facet | Durastante, Fabio Giscard, Pierre-Louis Pozza, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations Durastante, Fabio Giscard, Pierre-Louis Pozza, Stefano Numerical Analysis 26A33, 65L05, 33C45 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. |
| title | A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations |
| topic | Numerical Analysis 26A33, 65L05, 33C45 |
| url | https://arxiv.org/abs/2507.16652 |