Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach

Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach

In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fi...

Full description

Bibliographic Details
Main Authors: KumSong Jong, HuiChol Choi, KyongJun Jang, SunAe Pak
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/2930892
id doaj-7d9cc55be5ba4ce1aed24609c82fd6a8
record_format Article
spelling doaj-7d9cc55be5ba4ce1aed24609c82fd6a82020-11-25T02:51:20ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/29308922930892Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions ApproachKumSong Jong0HuiChol Choi1KyongJun Jang2SunAe Pak3Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of KoreaFaculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of KoreaFaculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of KoreaFaculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of KoreaIn this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. And by employing the upper and lower solutions technique, we derive a new approach to obtain the maximal and minimal solutions to the given problem. Finally, we present some examples to demonstrate our existence and uniqueness results.http://dx.doi.org/10.1155/2020/2930892
collection DOAJ
language English
format Article
sources DOAJ
author KumSong Jong
HuiChol Choi
KyongJun Jang
SunAe Pak
spellingShingle KumSong Jong
HuiChol Choi
KyongJun Jang
SunAe Pak
Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
Journal of Function Spaces
author_facet KumSong Jong
HuiChol Choi
KyongJun Jang
SunAe Pak
author_sort KumSong Jong
title Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
title_short Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
title_full Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
title_fullStr Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
title_full_unstemmed Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach
title_sort existence and uniqueness results for a class of singular fractional boundary value problems with the p-laplacian operator via the upper and lower solutions approach
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. And by employing the upper and lower solutions technique, we derive a new approach to obtain the maximal and minimal solutions to the given problem. Finally, we present some examples to demonstrate our existence and uniqueness results.
url http://dx.doi.org/10.1155/2020/2930892
work_keys_str_mv AT kumsongjong existenceanduniquenessresultsforaclassofsingularfractionalboundaryvalueproblemswiththeplaplacianoperatorviatheupperandlowersolutionsapproach
AT huicholchoi existenceanduniquenessresultsforaclassofsingularfractionalboundaryvalueproblemswiththeplaplacianoperatorviatheupperandlowersolutionsapproach
AT kyongjunjang existenceanduniquenessresultsforaclassofsingularfractionalboundaryvalueproblemswiththeplaplacianoperatorviatheupperandlowersolutionsapproach
AT sunaepak existenceanduniquenessresultsforaclassofsingularfractionalboundaryvalueproblemswiththeplaplacianoperatorviatheupperandlowersolutionsapproach
_version_ 1715369461605728256

Similar Items