{"title":"Dynamical Behaviour of a Fractional-order SEIB Model","authors":"Tasmia Roshan, Surath Ghosh, Sunil Kumar","doi":"10.1007/s10773-024-05724-6","DOIUrl":null,"url":null,"abstract":"<p>In this study, we first take the integer order model and then extend it using the fractional operator due to the benefits of the fractional derivative. Next, we discuss the SEIB model in a fractional framework with the Atangana-Baleanu-Caputo derivative and examine its dynamics. The existence and uniqueness of model solutions are investigated using fixed-point theory. After that, we apply the fractal-fractional notation with the Atangana-Baleanu derivative to the SEIB model and find that it has a unique solution. Different fractal and fractional order values are used to depict graphical representations. We also compare the considered operators using two distinct numerical schemes with various fractional order values. Further we conclude the fractal-fractional technique is superior to the fractional operator.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05724-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we first take the integer order model and then extend it using the fractional operator due to the benefits of the fractional derivative. Next, we discuss the SEIB model in a fractional framework with the Atangana-Baleanu-Caputo derivative and examine its dynamics. The existence and uniqueness of model solutions are investigated using fixed-point theory. After that, we apply the fractal-fractional notation with the Atangana-Baleanu derivative to the SEIB model and find that it has a unique solution. Different fractal and fractional order values are used to depict graphical representations. We also compare the considered operators using two distinct numerical schemes with various fractional order values. Further we conclude the fractal-fractional technique is superior to the fractional operator.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.