通过调整分数 M 衍射处理分数延迟微分问题的计算正交移位 Legendre-Galerkin 方法

IF 1.5 4区 物理与天体物理 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Hind Sweis, Omar Abu Arqub
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引用次数: 0

摘要

本文介绍了一种处理延迟分式微分问题的数值程序,该程序采用 M 分式方法定义导数。所提出的方案工作方式基于移位 Legendre-Galerkin 程序,该程序是解决广义分数导数复杂微分模型的有力工具。该方法包括构建一系列 Legendre 多项式,这些多项式构成了近似所需问题解的基函数。在求解由 Galerkin 方法产生的线性代数系统后,可获得数列的系数。数值精度和收敛性评估也与各种结果一起呈现。为验证过程的真实性和精确性,还进行了基于模拟的分析。结果表明,M 衍射和 Galerkin 实践为处理 M 延迟分数问题提供了替代性创新方法。最后还展示了一些关键问题和未来建议,并选取了一些参考文献。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The computational orthogonal shifted Legendre–Galerkin approach for handling fractional delay differential problems via adapting fractional M-derivative

This paper presents a numerical procedure for handling delay fractional differential problems where the derivative is defined using the M-fractional approach. The proposed scheme modus operandi is based on the shifted Legendre–Galerkin procedure, which is a powerful tool for solving complex differential models of generalized fractional derivatives. The method involves constructing a series of Legendre polynomials that form the basis functions for approximating the solution of the required problem. The coefficients of the series are obtained after solving an algebraic system of linear types that results from the application of the Galerkin practice. The numerical accuracy and convergence assessment are also presented together with various results. Simulations-based analyses are realized to validate the truthfulness and exactness of the process. The results manifest that the M-derivatives and the Galerkin practice provide alternative innovative approaches for handling M-delay fractional problems. Several keynotes and future recommendations are exhibited at the last with some selected references.

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来源期刊
International Journal of Modern Physics C
International Journal of Modern Physics C 物理-计算机:跨学科应用
CiteScore
3.00
自引率
15.80%
发文量
158
审稿时长
4 months
期刊介绍: International Journal of Modern Physics C (IJMPC) is a journal dedicated to Computational Physics and aims at publishing both review and research articles on the use of computers to advance knowledge in physical sciences and the use of physical analogies in computation. Topics covered include: algorithms; computational biophysics; computational fluid dynamics; statistical physics; complex systems; computer and information science; condensed matter physics, materials science; socio- and econophysics; data analysis and computation in experimental physics; environmental physics; traffic modelling; physical computation including neural nets, cellular automata and genetic algorithms.
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