Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI:10.1002/mma.10420

Yadollah Ordokhani, Sedigheh Sabermahani, Parisa Rahimkhani

引用次数: 0

Abstract

Fractional-order ray equations and fractional Duffing-van der Pol oscillator equations are relationships utilized as a reliable means of modeling some phenomena in optics and engineering. The main motivation of this study is to introduce a new hybrid technique utilizing Chelyshkov wavelets and least squares-support vector regression (LS-SVR) for determining the approximate solution of fractional ray equations and fractional Duffing-van der Pol oscillator equations (D-v POEs). With the help of the Riemann-Liouville operator for Chelyshkov wavelets and LS-SVR (called Chw-Ls-SVR), the mentioned problems transform into systems of algebraic equations. The convergence analysis is discussed. Finally, the numerical results are proposed and compared with some schemes to display the capability of the numerical technique proposed here.

查看原文本刊更多论文

应用切利什科夫小波和最小二乘支持向量回归求解光学和工程学中出现的分数微分方程

分数阶射线方程和分数 Duffing-van der Pol 振荡器方程是光学和工程学中某些现象建模的可靠方法。本研究的主要动机是引入一种新的混合技术，利用切利什科夫小波和最小二乘支持向量回归（LS-SVR）来确定分数射线方程和分数达芬-范德波尔振荡器方程（D-v POEs）的近似解。借助用于 Chelyshkov 小波和 LS-SVR（称为 Chw-Ls-SVR）的黎曼-柳维尔算子，上述问题转化为代数方程系统。讨论了收敛分析。最后，提出了数值结果，并与一些方案进行了比较，以显示本文提出的数值技术的能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.