减少高分数阶系统的稳健方案

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Journal of Engineering Mathematics Pub Date : 2023-12-08 DOI:10.1007/s10665-023-10310-6

Iqbal M. Batiha, Nadia Allouch, Iqbal H. Jebril, Shaher Momani

{"title":"减少高分数阶系统的稳健方案","authors":"Iqbal M. Batiha, Nadia Allouch, Iqbal H. Jebril, Shaher Momani","doi":"10.1007/s10665-023-10310-6","DOIUrl":null,"url":null,"abstract":"The objective of this work is to present a numerical solution to a system of higher fractional-order differential equations with initial value problems. In order to achieve this objective, we develop a novel theoretical result aimed to reduce these higher fractional-order systems to \\(\\alpha \\)-fractional systems, where \\(0<\\alpha \\le 1\\), and then apply a recent numerical approach called modified fractional Euler method, which is regarded a numerical modification of the fractional Euler Method (FEM). Finally, we will give numerical applications to illustrate our results using MATLAB procedures.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A robust scheme for reduction of higher fractional-order systems\",\"authors\":\"Iqbal M. Batiha, Nadia Allouch, Iqbal H. Jebril, Shaher Momani\",\"doi\":\"10.1007/s10665-023-10310-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The objective of this work is to present a numerical solution to a system of higher fractional-order differential equations with initial value problems. In order to achieve this objective, we develop a novel theoretical result aimed to reduce these higher fractional-order systems to \\\\(\\\\alpha \\\\)-fractional systems, where \\\\(0<\\\\alpha \\\\le 1\\\\), and then apply a recent numerical approach called modified fractional Euler method, which is regarded a numerical modification of the fractional Euler Method (FEM). Finally, we will give numerical applications to illustrate our results using MATLAB procedures.\",\"PeriodicalId\":50204,\"journal\":{\"name\":\"Journal of Engineering Mathematics\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Engineering Mathematics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s10665-023-10310-6\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Engineering Mathematics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s10665-023-10310-6","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

这项工作的目的是提出一个带初值问题的高分数阶微分方程系统的数值解。为了实现这一目标，我们提出了一个新颖的理论结果，旨在将这些高分数阶系统简化为 \(\alpha \)-分数系统，其中 \(0<\alpha \le 1\)，然后应用一种称为修正分数欧拉法的最新数值方法，该方法被视为分数欧拉法（FEM）的数值修正。最后，我们将利用 MATLAB 程序给出数值应用来说明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A robust scheme for reduction of higher fractional-order systems

The objective of this work is to present a numerical solution to a system of higher fractional-order differential equations with initial value problems. In order to achieve this objective, we develop a novel theoretical result aimed to reduce these higher fractional-order systems to \(\alpha \)-fractional systems, where \(0<\alpha \le 1\), and then apply a recent numerical approach called modified fractional Euler method, which is regarded a numerical modification of the fractional Euler Method (FEM). Finally, we will give numerical applications to illustrate our results using MATLAB procedures.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Engineering Mathematics 工程技术-工程：综合

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： The aim of this journal is to promote the application of mathematics to problems from engineering and the applied sciences. It also aims to emphasize the intrinsic unity, through mathematics, of the fundamental problems of applied and engineering science. The scope of the journal includes the following: • Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional−analytic methods, Numerical analysis, Computational methods. • Applied Fields: Continuum mechanics, Stability theory, Wave propagation, Diffusion, Heat and mass transfer, Free−boundary problems; Fluid mechanics: Aero− and hydrodynamics, Boundary layers, Shock waves, Fluid machinery, Fluid−structure interactions, Convection, Combustion, Acoustics, Multi−phase flows, Transition and turbulence, Creeping flow, Rheology, Porous−media flows, Ocean engineering, Atmospheric engineering, Non-Newtonian flows, Ship hydrodynamics; Solid mechanics: Elasticity, Classical mechanics, Nonlinear mechanics, Vibrations, Plates and shells, Fracture mechanics; Biomedical engineering, Geophysical engineering, Reaction−diffusion problems; and related areas. The Journal also publishes occasional invited ''Perspectives'' articles by distinguished researchers reviewing and bringing their authoritative overview to recent developments in topics of current interest in their area of expertise. Authors wishing to suggest topics for such articles should contact the Editors-in-Chief directly. Prospective authors are encouraged to consult recent issues of the journal in order to judge whether or not their manuscript is consistent with the style and content of published papers.