{"title":"Existence of an initial value problem for time-fractional Oldroyd-B fluid equation using Banach fixed point theorem","authors":"Vo Viet Tri","doi":"10.31197/atnaa.943242","DOIUrl":null,"url":null,"abstract":"In this paper, we study the initial boundary value problem for time-fractional Oldroyd-B fluid equation. Our model contains two Riemann-Liouville fractional derivatives which have many applications, for example, in viscoelastic flows. For the linear case, we obtain regularity results under some different assumptions of the initial data and the source function. For the non-linear case, we obtain the existence of a unique solution using Banach’s fixed point theorem.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in the Theory of Nonlinear Analysis and its Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31197/atnaa.943242","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we study the initial boundary value problem for time-fractional Oldroyd-B fluid equation. Our model contains two Riemann-Liouville fractional derivatives which have many applications, for example, in viscoelastic flows. For the linear case, we obtain regularity results under some different assumptions of the initial data and the source function. For the non-linear case, we obtain the existence of a unique solution using Banach’s fixed point theorem.