Numerical Solution of Variable-Order Fractional Bagley-Torvik Equation Using Multi-Domain Legendre Collocation Approach

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

2 Department of Mathematics, Faculty of Sciences, Sahand University of Technology, Tabriz, Iran.

10.22034/cmde.2025.70146.3472

Abstract

This paper introduces a novel multi-domain Legendre-collocation method for the numerical solution of the variable-order fractional Bagley-Torvik equation. To address the computational challenges posed by variable-order fractional derivatives and their weakly singular kernels, an operational matrix formulation is developed, providing a highly efficient alternative to classical three-term recurrence schemes based on Legendre polynomials. The domain decomposition strategy enables local evaluation of the memory integral within each subdomain, thereby preserving spectral accuracy while mitigating the stability degradation and round-off error accumulation often encountered in global spectral methods over extended intervals. Numerical experiments confirm the proposed method's spectral convergence, stability, and computational efficiency. The results highlight the method's potential as a reliable and accurate framework for solving a broad class of variable-order fractional differential equations.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 January 2026

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History

  • Receive Date: 09 November 2025
  • Revise Date: 24 December 2025
  • Accept Date: 31 December 2025

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