Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions

被引：30

作者：

Guo, Limin ^{[1
]}

Liu, Lishan ^{[1
,2
]}

Wu, Yonghong ^{[2
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia

来源：

BOUNDARY VALUE PROBLEMS | 2016年

基金：

中国国家自然科学基金;

关键词：

fractional differential equation; singular problem; infinite-point boundary conditions; positive solution; sequential techniques and regularization; EIGENVALUE;

D O I：

10.1186/s13661-016-0621-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a class of singular fractional differential equations with infinite-point boundary conditions. The fractional orders are involved in the nonlinearity of the boundary value problem, and the nonlinearity is allowed to be singular with respect to not only the time variable but also to the space variable. Firstly, we give Green's function and establish its properties. Then, we utilize the sequential technique and regularization to investigate the existence of positive solutions. Finally, we give an example of application of our result.

引用

页数：22

共 24 条

[1] Positive solutions for Dirichlet problems, of singular nonlinear fractional differential equations [J].

Agarwal, Ravi P. ;

O'Regan, Donal ;

Stanek, Svatoslav .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 371 (01) :57-68

[2]

[Anonymous], 1993, INTRO FRACTIONAL CA

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4]

Bai Z, 2005, J MATH ANAL APPL, V311, P2761

[5] Existence and multiplicity of positive solutions for singular fractional boundary value problems [J].

Bai, Zhanbing ;

Sun, Weichen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (09) :1369-1381

[6] Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann-Stieltjes Integrals [J].

Jiang, Jiqiang ;

Liu, Lishan ;

Wu, Yonghong .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[7] Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions [J].

Jiang, Jiqiang ;

Liu, Lishan ;

Wu, Yonghong .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[8]

Jing W., 2013, APPL MATH COMPUT, V41, P171

[9]

Kibas AA., 2006, THEORY APPL FRACTION

[10] Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis [J].

Kou, Chunhai ;

Zhou, Huacheng ;

Yan, Ye .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) :5975-5986

← 1 2 3 →