Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator
This article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/2319062 |
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| author | Fang Wang Lishan Liu Yonghong Wu Yumei Zou |
| author_facet | Fang Wang Lishan Liu Yonghong Wu Yumei Zou |
| author_sort | Fang Wang |
| collection | DOAJ |
| description | This article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary conditions, and different fractional orders are involved in the boundary conditions and the nonlinear term, respectively. Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. And we obtain the dependence of solution upon parameter. Furthermore, two numerical examples are presented to illustrate the application of our main results. |
| format | Article |
| id | doaj-art-1cff2a08e3d1429984ce6faeccad2eff |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-1cff2a08e3d1429984ce6faeccad2eff2025-02-03T06:01:46ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/23190622319062Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian OperatorFang Wang0Lishan Liu1Yonghong Wu2Yumei Zou3School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaDepartment of Mathematics and Statistics, Curtin University, Perth, WA 6845, AustraliaDepartment of Statistics and Finance, Shandong University of Science and Technology, Qingdao 266590, ChinaThis article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary conditions, and different fractional orders are involved in the boundary conditions and the nonlinear term, respectively. Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. And we obtain the dependence of solution upon parameter. Furthermore, two numerical examples are presented to illustrate the application of our main results.http://dx.doi.org/10.1155/2019/2319062 |
| spellingShingle | Fang Wang Lishan Liu Yonghong Wu Yumei Zou Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator Complexity |
| title | Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator |
| title_full | Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator |
| title_fullStr | Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator |
| title_full_unstemmed | Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator |
| title_short | Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator |
| title_sort | iterative analysis of the unique positive solution for a class of singular nonlinear boundary value problems involving two types of fractional derivatives with p laplacian operator |
| url | http://dx.doi.org/10.1155/2019/2319062 |
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