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arXiv · 2508.08067

The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation

Francesco Dell'Accio·Filomena Di Tommaso·Ilde Ferrara
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Abstract

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.

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Francesco Dell'Accio, Filomena Di Tommaso, Ilde Ferrara. 2025-08-11. The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation. https://arxiv.org/abs/2508.08067

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