Wadhah Ahmed Alsadi, Wadhah Mokhtar Hussein, T. Q. S. Abdullah
{"title":"Existence and stability criterion for the results of fractional order $ Phi_{p} $-Laplacian operator boundary value problem","authors":"Wadhah Ahmed Alsadi, Wadhah Mokhtar Hussein, T. Q. S. Abdullah","doi":"10.22034/CMDE.2021.32807.1580","DOIUrl":null,"url":null,"abstract":"In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with $ Phi_{p} $-Laplacian operator. Our problem is based on Caputo fractional derivative of orders $ sigma,epsilon$, where $ k- 1<sigma,epsilonleq k $, and $ kgeq3 $. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2021.32807.1580","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with $ Phi_{p} $-Laplacian operator. Our problem is based on Caputo fractional derivative of orders $ sigma,epsilon$, where $ k- 1