A New Approach to Least Squares Support Vector Regression Using the Legendre Operational Matrix for Solving Fractional Fredholm Integro-Differential Equations

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-09-25 Epub Date: 2026-07-24 DOI:10.1002/mma.70871

Marzieh Pourbabaee, Abbas Saadatmandi

引用次数: 0

Abstract

In this study, a novel hybrid technique is introduced to address linear and nonlinear fractional Fredholm integro-differential equations (FFIDEs) by utilizing least squares support vector regression (LS-SVR) along with the Legendre operational matrix of fractional derivatives (OMFD). The unknown function is represented as a linear combination of shifted Legendre polynomials. Also, the Galerkin and collocation spectral methods are used. We then formulate an optimization problem and convert it into a set of algebraic equations. To address a linear FFIDE, we introduced a matrix representation of the dual problem and demonstrated the resulting linear systems. Also, a discussion on error estimates is included. Finally, to demonstrate the validity and applicability of the suggested methods, some test examples are presented.

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用Legendre操作矩阵求解分数阶Fredholm积分微分方程的最小二乘支持向量回归新方法

本文采用最小二乘支持向量回归（LS-SVR）和Legendre分数阶导数运算矩阵（OMFD）相结合的混合方法求解线性和非线性分数阶Fredholm积分微分方程（FFIDEs）。未知函数表示为移位的勒让德多项式的线性组合。此外，还采用了伽辽金谱法和搭配谱法。然后，我们将最优化问题形式化，并将其转化为一组代数方程。为了解决线性FFIDE问题，我们引入了对偶问题的矩阵表示，并演示了得到的线性系统。此外，还对误差估计进行了讨论。最后，通过算例验证了所提方法的有效性和适用性。

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.