{"title":"Green’s Functions for a Fractional Boundary Value Problem with Three Terms","authors":"P. Eloe, Jeffrey T. Neugebauer","doi":"10.3390/foundations2040060","DOIUrl":null,"url":null,"abstract":"We construct a Green’s function for the three-term fractional differential equation −D0+α−1u+aD0+μu+f(t)u=h(t), 0<t<b, where α∈(2,3], μ∈(1,2], and f is continuous, satisfying the boundary conditions u(0)=u′(0)=0, D0+βu(b)=0, where β∈[0,2]. To accomplish this, we first construct a Green’s function for the two-term problem −D0+α−1u+aD0+μu=h(t), 0<t<b, satisfying the same boundary conditions. A lemma from spectral theory is integral to our construction. Some limiting properties of the Green’s function for the two-term problem are also studied. Finally, existence results are given for a nonlinear problem.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/foundations2040060","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
We construct a Green’s function for the three-term fractional differential equation −D0+α−1u+aD0+μu+f(t)u=h(t), 0
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