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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/2930892 |
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| author | KumSong Jong HuiChol Choi KyongJun Jang SunAe Pak |
| author_facet | KumSong Jong HuiChol Choi KyongJun Jang SunAe Pak |
| author_sort | KumSong Jong |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-7d9cc55be5ba4ce1aed24609c82fd6a8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7d9cc55be5ba4ce1aed24609c82fd6a82025-02-03T01:28:42ZengWileyJournal 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 |
| 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 |
| 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_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_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_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 |
| url | http://dx.doi.org/10.1155/2020/2930892 |
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