PofoliaShared via Pofolia

Fractional Calculus and Applied Analysis· 2026Q1

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

Francesco Dell’Accio, Filomena Di Tommaso, Ilde Ferrara

Short summary

A new univariate multinode Shepard method accurately approximates Caputo fractional derivatives, solving Bagley–Torvik equations with competitive accuracy compared to existing methods.

AI-generated from the title and abstract; the full text is not read.

Key points

  • A univariate multinode Shepard operator is proposed for approximating Caputo fractional derivatives.
  • Gauss–Jacobi quadrature is used for fractional integral evaluation.
  • The method is applied to Bagley–Torvik boundary and initial value problems.
  • Numerical experiments show high accuracy for polynomial and non-polynomial solutions.
  • The method achieves competitive accuracy compared to existing numerical methods.

AI-generated from the title and abstract; the full text is not read.

Abstract

Abstract In this paper, we propose a numerical approach based on the univariate multinode Shepard operator for the approximation of Caputo fractional derivatives. The fractional integral is evaluated through a Gauss–Jacobi quadrature formula, and the resulting approximation is then employed within a collocation scheme for Bagley–Torvik boundary and initial value problems. Approximation and convergence properties are discussed, together with the influence of the conditioning of the associated collocation systems. Numerical experiments involving different node distributions show high accuracy for both polynomial and non-polynomial solutions. The method is also applied to variable-coefficient and nonsmooth Bagley–Torvik problems, and comparisons with previously published numerical methods confirm its competitive accuracy.

The authors' abstract, as published at the source. Fractional Calculus and Applied Analysis, 2026 · DOI ↗

TakeawaysPremium
Ask the paperFree account

Continue with a free account

Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.

Continue free on the web

Sign in with Google or Apple; no card needed. You come back to this paper.

On your phone:

Get it on Google Play Download on the App Store

Field: Modeling and Simulation

Modeling and SimulationMathematics