利用分数阶切利什科夫函数求解分数延迟微分方程的有效数值方法

IF 1.7 4区 数学 Q1 Mathematics
A. I. Ahmed, M. S. Al-Sharif
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引用次数: 0

摘要

本文利用分数阶切利什科夫函数(FCHFs)和黎曼-黎奥维尔分数积分,将问题转化为带有未知 FCHFs 系数的代数方程系统,从而找到分数延迟微分方程的数值解。估算了 FCHFs 近似的误差范围,并证明了其收敛性。通过几个例子证明了所提出方法的有效性和准确性。即使精确解不是多项式,所得到的解也是精确的,并且与精确解一致。此外,还显示了所获得的数值结果与近期文献报道的结果之间的比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An effective numerical method for solving fractional delay differential equations using fractional-order Chelyshkov functions
In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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