{"title":"Existence of Solutions for the Boundary Value Problem","authors":"Liu Xiao-bo","doi":"10.1142/9789811213755_0022","DOIUrl":null,"url":null,"abstract":"The existing of solutions for the following boundary value problem of fractional differential equations is studied.{cDαu(t) +λcDα-1u(t) +f(t,u(t) ) =0,0t1,u(0) =0,u(1) =0,where 1α≤2,0≤λ18,cDα is Caputo fractional derivative,and f∶[0,1]×R→R is continuous.Under several types of sufficient conditions,the existence of solutions to the above problem is proved by a fixed-point theorems.","PeriodicalId":39680,"journal":{"name":"Journal of Donghua University (English Edition)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Donghua University (English Edition)","FirstCategoryId":"1087","ListUrlMain":"https://doi.org/10.1142/9789811213755_0022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The existing of solutions for the following boundary value problem of fractional differential equations is studied.{cDαu(t) +λcDα-1u(t) +f(t,u(t) ) =0,0t1,u(0) =0,u(1) =0,where 1α≤2,0≤λ18,cDα is Caputo fractional derivative,and f∶[0,1]×R→R is continuous.Under several types of sufficient conditions,the existence of solutions to the above problem is proved by a fixed-point theorems.
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