{"title":"A robust stability criterion in the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative","authors":"R. Temoltzi-Ávila","doi":"10.1007/s11587-024-00861-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present a robust stability criterion for the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative. The criterion is obtained by extending a concept of stability under constant-acting perturbations that is regularly applied to systems of differential equations of integer order. We assume the existence of uncertainty in the subdiffusion equation due to the effect of external sources that are represented by Fourier series whose generalized Fourier coefficients are absolutely continuous and bounded functions. The results obtained suggest that the robust stability criterion allows us to guarantee that the solution of the subdiffusion equation, as well as its Caputo–Fabrizio fractional derivative and its first partial derivative with respect to the longitudinal axis, are bounded by a constant whose value is initially established. The results obtained are illustrated numerically.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-15","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/s11587-024-00861-w","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
Abstract
In this paper, we present a robust stability criterion for the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative. The criterion is obtained by extending a concept of stability under constant-acting perturbations that is regularly applied to systems of differential equations of integer order. We assume the existence of uncertainty in the subdiffusion equation due to the effect of external sources that are represented by Fourier series whose generalized Fourier coefficients are absolutely continuous and bounded functions. The results obtained suggest that the robust stability criterion allows us to guarantee that the solution of the subdiffusion equation, as well as its Caputo–Fabrizio fractional derivative and its first partial derivative with respect to the longitudinal axis, are bounded by a constant whose value is initially established. The results obtained are illustrated numerically.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
