{"title":"边值问题解的存在性","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":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"1 1\",\"pages\":\"\"},\"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}","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}
Existence of Solutions for the Boundary Value Problem
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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