The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation
Numerical Analysis
2025-08-12 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2508.08067,
title = {The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation},
author = {Francesco Dell'Accio and Filomena Di Tommaso and Ilde Ferrara},
journal= {arXiv preprint arXiv:2508.08067},
year = {2025}
}