分形样条曲线的卡普托分数导数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-05 DOI:10.1007/s11075-024-01875-z

T. M. C. Priyanka, A. Gowrisankar, M. Guru Prem Prasad, Yongshun Liang, Jinde Cao

{"title":"分形样条曲线的卡普托分数导数","authors":"T. M. C. Priyanka, A. Gowrisankar, M. Guru Prem Prasad, Yongshun Liang, Jinde Cao","doi":"10.1007/s11075-024-01875-z","DOIUrl":null,"url":null,"abstract":"The Caputo fractional derivative of a real continuous function g distinguishes from the other fractional derivative methods with the demand for the existence of its first order derivative \$g'\$. This attribute leads to the investigation of Caputo fractional derivative of \$\\alpha \$-fractal splines rather than just a continuous non-differentiable \$\\alpha \$-fractal function. A bounded linear operator corresponding to the Caputo fractional derivative of fractal version is reported. In addition, a new family of fractal perturbations is proposed in association with the fractional derivative. Thereafter, a numerical approach is used to determine the exact Caputo fractional derivative of fractal functions in terms of Legendre polynomials.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Caputo fractional derivative of $$\\\\alpha $$ -fractal spline\",\"authors\":\"T. M. C. Priyanka, A. Gowrisankar, M. Guru Prem Prasad, Yongshun Liang, Jinde Cao\",\"doi\":\"10.1007/s11075-024-01875-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Caputo fractional derivative of a real continuous function g distinguishes from the other fractional derivative methods with the demand for the existence of its first order derivative \\\$g'\\\$. This attribute leads to the investigation of Caputo fractional derivative of \\\$\\\\alpha \\\$-fractal splines rather than just a continuous non-differentiable \\\$\\\\alpha \\\$-fractal function. A bounded linear operator corresponding to the Caputo fractional derivative of fractal version is reported. In addition, a new family of fractal perturbations is proposed in association with the fractional derivative. Thereafter, a numerical approach is used to determine the exact Caputo fractional derivative of fractal functions in terms of Legendre polynomials.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11075-024-01875-z\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01875-z","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

实连续函数 g 的卡普托分数导数与其他分数导数方法不同，它要求存在一阶导数 $g'$。这一特性导致了对$\α$-分形样条的卡普托分形导数的研究，而不仅仅是对$\α$-分形函数的连续无差导数的研究。报告了与分形版本的卡普托分形导数相对应的有界线性算子。此外，还提出了与分形导数相关的新的分形扰动系列。此后，利用数值方法确定了分形函数的精确卡普托分形导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Caputo fractional derivative of $$\alpha $$ -fractal spline$

查看原文本刊更多论文

Caputo fractional derivative of $$\alpha $$ -fractal spline

The Caputo fractional derivative of a real continuous function g distinguishes from the other fractional derivative methods with the demand for the existence of its first order derivative $g'$. This attribute leads to the investigation of Caputo fractional derivative of $\alpha $-fractal splines rather than just a continuous non-differentiable $\alpha $-fractal function. A bounded linear operator corresponding to the Caputo fractional derivative of fractal version is reported. In addition, a new family of fractal perturbations is proposed in association with the fractional derivative. Thereafter, a numerical approach is used to determine the exact Caputo fractional derivative of fractal functions in terms of Legendre polynomials.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.