一种精确模拟分数阶时滞微分方程的方法

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2023-09-05 DOI:10.3390/fractalfract7090671

Mohamed Adel, M. Khader, Salman Algelany, Khaled Aldwoah

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引用次数: 0

摘要

我们提出的分数阶勒让德多项式(FLPs)是求解分数阶延迟微分方程(FDDEs)的有效方法。刘维尔-卡普托意义被用来描述分数阶导数。该方法采用基于FLPs的光谱配置技术。该方法将FDDEs转换为一组代数方程。我们研究了收敛性分析，并给出了近似解的误差上界。举例说明了所建议方法的精确性。

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An Accurate Approach to Simulate the Fractional Delay Differential Equations

The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach.

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.