Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with mixed-type boundary value conditions

被引：15
作者：
Wang, Fang [1 ]
Liu, Lishan [1 ,3 ]
Kong, Debin [2 ]
Wu, Yonghong [3 ]
机构：
[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
[2] Yantai Nanshan Univ, Dept Math & Phys, Yantai 265713, Shandong, Peoples R China
[3] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia
来源：
NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2019年 / 24卷 / 01期
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
fractional differential equations; mixed-type boundary value problem; positive solution; unique positive solution; SYSTEM MODEL;
D O I：
10.15388/NA.2019.1.5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we study a class of nonlinear fractional differential equations with mixed-type boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction mapping principle based on some available operators, we obtain the existence of positive solutions and a unique positive solution of the problem. Finally, two examples are given to demonstrate the validity of our main results.
引用
收藏
页码：73 / 94
页数：22
相关论文
共 37 条
  • [1] Nonlinear fractional differential equations with integral boundary value conditions
    Cabada, Alberto
    Hamdi, Zakaria
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 228 : 251 - 257
  • [2] Positive solutions of nonlinear fractional differential equations with integral boundary value conditions
    Cabada, Alberto
    Wang, Guotao
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) : 403 - 411
  • [3] Uniqueness of solution for boundary value problems for fractional differential equations
    Cui, Yujun
    [J]. APPLIED MATHEMATICS LETTERS, 2016, 51 : 48 - 54
  • [4] Existence of a positive solution to a class of fractional differential equations
    Goodrich, Christopher S.
    [J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (09) : 1050 - 1055
  • [5] Guo D., 1988, Nonlinear problems in abstract cones
  • [6] Guo D., 1987, Nonlinear Integral Equations
  • [7] Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters
    Guo, Limin
    Liu, Lishan
    Wu, Yonghong
    [J]. NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2018, 23 (02): : 182 - 203
  • [8] Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions
    Guo, Limin
    Liu, Lishan
    Wu, Yonghong
    [J]. BOUNDARY VALUE PROBLEMS, 2016,
  • [9] Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions
    Guo, Limin
    Liu, Lishan
    Wu, Yonghong
    [J]. BOUNDARY VALUE PROBLEMS, 2016,
  • [10] Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions
    Guo, Limin
    Liu, Lishan
    Wu, Yonghong
    [J]. NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2016, 21 (05): : 635 - 650
1234