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
type: Item
instance of: scholarly article
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
zbMATH Open document ID: 1440.34012
DOI: 10.1155/2019/2319062
author: Fang Wang
author: Lishan Liu
author: Yumei Zou
author: Yonghong Wu
published in: Complexity
publication date: 2019-11-25T00:00:00Z
review text: Summary: 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 with 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.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7136307
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/2319062
OpenAlex ID: W2981874938
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description: scientific article; zbMATH DE number 7136307