The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911101632905216 |
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| author | Dell'Accio, Francesco Di Tommaso, Filomena Ferrara, Ilde |
| author_facet | Dell'Accio, Francesco Di Tommaso, Filomena Ferrara, Ilde |
| contents | In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently, the proposed method is applied to the numerical solution of boundary value problems (BVPs) and initial value problems (IVPs), specifically addressing the Bagley-Torvik equations. Experimental results confirm the method's effectiveness, particularly in accurately approximating the Bagley-Torvik equation for both BVPs and IVPs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation Dell'Accio, Francesco Di Tommaso, Filomena Ferrara, Ilde Numerical Analysis In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently, the proposed method is applied to the numerical solution of boundary value problems (BVPs) and initial value problems (IVPs), specifically addressing the Bagley-Torvik equations. Experimental results confirm the method's effectiveness, particularly in accurately approximating the Bagley-Torvik equation for both BVPs and IVPs. |
| title | The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.08067 |