Ali El Mfadel, Fatima Ezzahra Bourhi̇m, M. Elomari
{"title":"Existence of mild solutions for semilinear $\\psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces","authors":"Ali El Mfadel, Fatima Ezzahra Bourhi̇m, M. Elomari","doi":"10.53006/rna.1121916","DOIUrl":null,"url":null,"abstract":"The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\\psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Nonlinear Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53006/rna.1121916","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.
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