Explicit Solution for the Bagley–Torvik Equation With Variable Coefficients

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-05 DOI:10.1002/mma.10862

Huiwen Wang, Fang Li

引用次数: 0

Abstract

Analytical solutions to the Bagley–Torvik equation with variable coefficients are difficult to be obtained, so most previous research focused on numerical solutions. In this paper, with the help of a fractional integral equation, we obtain an explicit representation of a unique exact solution of the initial value problem for the Bagley–Torvik equation with variable coefficients in a weighted space. We present three examples and give numerical simulations as an application.

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变系数Bagley-Torvik方程的显式解

变系数Bagley-Torvik方程的解析解很难求出，因此以往的研究大多集中在数值解上。本文利用分数阶积分方程，给出了变系数Bagley-Torvik方程初值问题的唯一精确解的显式表示。我们给出了三个例子，并给出了数值模拟作为应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.