{"title":"具有积分初始条件的非局部分数Cauchy问题概周期解的存在性","authors":"S. Maghsoodi, A. Neamaty","doi":"10.32513/tmj/19322008150","DOIUrl":null,"url":null,"abstract":"In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition\",\"authors\":\"S. Maghsoodi, A. Neamaty\",\"doi\":\"10.32513/tmj/19322008150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.\",\"PeriodicalId\":43977,\"journal\":{\"name\":\"Tbilisi Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tbilisi Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32513/tmj/19322008150\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tbilisi Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32513/tmj/19322008150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition
In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.
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