Work

Numerical Solutions for Fractional Bagley–Torvik Equation with Integral Boundary Conditions

Year: 2025

Type: article

Abstract: The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE poses additional difficulties, and efficient approaches for handling nonlinear terms are still lacking in the literature. This study proposes an improved numerical method for the fractional BTE with integral boundary conditions. By employing an integration technique, the original problem is transformed into a weakly singular Fredholm–Hammerstein (F–H) integral equation of the second kind. To address the nonlinear terms, an enhanced piecewise Taylor expansion scheme is developed to construct the discrete form, while the uniqueness of the solution is proven using the contraction mapping theorem in Banach spaces. The convergence and error analyses are rigorously carried out, and numerical experiments confirm the accuracy and efficiency of the proposed approach.

Source: Symmetry

DOI: 10.3390/sym17101755

Authors: Xueling Liu, Jing Huang, Junlin Li, Yufeng Zhang

Institutions: Bozhou University, Fuyang Normal University, Beijing University of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, University Natural Science Research Project of Anhui Province, Doctoral Foundation of Fuyang Normal University