分数阶时间导数对比例时滞的模拟,用于求解和研究广义摄动kdv方程

IF 2.4 Q2 ENGINEERING, MECHANICAL
M. Alquran, Mohammed Ali, Kamel Al-khaled, G. Grossman
{"title":"分数阶时间导数对比例时滞的模拟,用于求解和研究广义摄动kdv方程","authors":"M. Alquran, Mohammed Ali, Kamel Al-khaled, G. Grossman","doi":"10.1515/nleng-2022-0282","DOIUrl":null,"url":null,"abstract":"Abstract In this study, the Caputo-type fractional time-derivative is simulated by inserting a proportional time-delay into the field function of the perturbed-KdV equation. Two effective methods have been adapted to obtain analytical solutions for this model. Then, independently, the effect of the fractional derivative and the proportional delay on the topological shape of the pKdV propagation was extrapolated. The significant conclusions of the current article reveal that the fractional derivative plays the same role as the presence of a proportional delay in the time coordinate if it is assigned as a substitute for it. With this, from a practical mathematical point of view, we have provided one of the geometric explanations of the fractional derivative. Finally, via the obtained approximate solution, we studied the impact of the perturbed coefficient on propagating the waves of the proposed KdV model.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":"67 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simulations of fractional time-derivative against proportional time-delay for solving and investigating the generalized perturbed-KdV equation\",\"authors\":\"M. Alquran, Mohammed Ali, Kamel Al-khaled, G. Grossman\",\"doi\":\"10.1515/nleng-2022-0282\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this study, the Caputo-type fractional time-derivative is simulated by inserting a proportional time-delay into the field function of the perturbed-KdV equation. Two effective methods have been adapted to obtain analytical solutions for this model. Then, independently, the effect of the fractional derivative and the proportional delay on the topological shape of the pKdV propagation was extrapolated. The significant conclusions of the current article reveal that the fractional derivative plays the same role as the presence of a proportional delay in the time coordinate if it is assigned as a substitute for it. With this, from a practical mathematical point of view, we have provided one of the geometric explanations of the fractional derivative. Finally, via the obtained approximate solution, we studied the impact of the perturbed coefficient on propagating the waves of the proposed KdV model.\",\"PeriodicalId\":37863,\"journal\":{\"name\":\"Nonlinear Engineering - Modeling and Application\",\"volume\":\"67 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Engineering - Modeling and Application\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/nleng-2022-0282\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0282","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

摘要

在本研究中,通过在扰动- kdv方程的场函数中插入比例时滞来模拟caputo型分数阶时间导数。采用了两种有效的方法来获得该模型的解析解。然后,分别外推分数阶导数和比例延迟对pKdV传播拓扑形状的影响。本文的重要结论表明,分数阶导数在时间坐标中扮演着与比例延迟相同的角色,如果它被指定为它的替代品。由此,从实用的数学观点出发,我们提供了分数阶导数的一种几何解释。最后,通过得到的近似解,我们研究了扰动系数对所提出的KdV模型的波传播的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simulations of fractional time-derivative against proportional time-delay for solving and investigating the generalized perturbed-KdV equation
Abstract In this study, the Caputo-type fractional time-derivative is simulated by inserting a proportional time-delay into the field function of the perturbed-KdV equation. Two effective methods have been adapted to obtain analytical solutions for this model. Then, independently, the effect of the fractional derivative and the proportional delay on the topological shape of the pKdV propagation was extrapolated. The significant conclusions of the current article reveal that the fractional derivative plays the same role as the presence of a proportional delay in the time coordinate if it is assigned as a substitute for it. With this, from a practical mathematical point of view, we have provided one of the geometric explanations of the fractional derivative. Finally, via the obtained approximate solution, we studied the impact of the perturbed coefficient on propagating the waves of the proposed KdV model.
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
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信