{"title":"A study on the finite time stability and controllability of time delay fractional model","authors":"P. K. Lakshmi Priya, K. Kaliraj","doi":"10.1007/s40065-025-00492-5","DOIUrl":null,"url":null,"abstract":"<div><p>The mainspring of this analytical study is to implement the idea of delayed argument cosine and sine conformable matrices to interpret the stability bounds of conformable type fractional operator over finite time period using modified integral form of Gronwall’s inequality. Further, we establish the conformable Grammian matrices in-terms of sine function to analyze the controllability results. The main inception is to first consider the linear controllability result of our defined system and to a greater extent, fixed point techniques along with the properties of Bochner-integral and inner product spaces are implemented to verify the controllability results of the nonlinear system. The theoretical study is graphically visualized using matlab software.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"155 - 170"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-025-00492-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The mainspring of this analytical study is to implement the idea of delayed argument cosine and sine conformable matrices to interpret the stability bounds of conformable type fractional operator over finite time period using modified integral form of Gronwall’s inequality. Further, we establish the conformable Grammian matrices in-terms of sine function to analyze the controllability results. The main inception is to first consider the linear controllability result of our defined system and to a greater extent, fixed point techniques along with the properties of Bochner-integral and inner product spaces are implemented to verify the controllability results of the nonlinear system. The theoretical study is graphically visualized using matlab software.
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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