Positive solutions for a boundary-value problem with Riemann-Liouville fractional derivative

被引：8
|
作者：
Xu, Jiafa [1 ]
Wei, Zhongli [1 ,2 ]
Ding, Youzheng [1 ,2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] Shandong Jianzhu Univ, Dept Math, Jinan 250101, Shandong, Peoples R China
来源：
LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 04期
关键词：
fractional boundary-value problem; positive solution; Krasnoselskii-Zabreiko fixed-point theorem; Riemann-Liouville derivative; DIFFERENTIAL-EQUATIONS; EXISTENCE;
D O I：
10.1007/s10986-012-9187-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we are mainly concerned with the existence of positive solutions for the fractional boundary-value problem Here alpha a (2, 3] is a real number, is the standard Riemann-Liouville fractional derivative of order alpha. By virtue of some inequalities associated with the fractional Green function for the above problem, without the assumption of the nonnegativity of f, we utilize the Krasnoselskii-Zabreiko fixed-point theorem to establish our main results. The interesting point lies in the fact that the nonlinear term is allowed to depend on u, u', and .
引用
收藏
页码：462 / 476
页数：15
相关论文
共 50 条
  • [41] On a final value problem for fractional reaction-diffusion equation with Riemann-Liouville fractional derivative
    Ngoc Tran
    Vo Van Au
    Zhou, Yong
    Nguyen Huy Tuan
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3086 - 3098
  • [42] Existence and Multiplicity of Positive Solutions for a Singular Riemann-Liouville Fractional Differential Problem
    Luca, Rodica
    FILOMAT, 2020, 34 (12) : 3931 - 3942
  • [43] PERIODIC BOUNDARY VALUE PROBLEMS WITH DELTA RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE ON TIME SCALES
    Yaslan, Ismail
    Liceli, Onur
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018,
  • [44] Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales
    Wu, Ling
    Zhu, Jiang
    ABSTRACT AND APPLIED ANALYSIS, 2013,
  • [45] On a backward problem for fractional diffusion equation with Riemann-Liouville derivative
    Nguyen Huy Tuan
    Nguyen Hoang Tuan
    Baleanu, Dumitru
    Tran Ngoc Thach
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (03) : 1292 - 1312
  • [46] Positive solutions for fractional differential systems with nonlocal Riemann-Liouville fractional integral boundary conditions
    Neamprem, Khomsan
    Muensawat, Thanadon
    Ntouyas, Sotiris K.
    Tariboon, Jessada
    POSITIVITY, 2017, 21 (03) : 825 - 845
  • [47] Anti-periodic boundary value problems of fractional differential equations with the Riemann-Liouville fractional derivative
    Guoqing Chai
    Advances in Difference Equations, 2013
  • [48] Anti-periodic boundary value problems of fractional differential equations with the Riemann-Liouville fractional derivative
    Chai, Guoqing
    ADVANCES IN DIFFERENCE EQUATIONS, 2013,
  • [49] Positive solutions for a Riemann-Liouville-type impulsive fractional integral boundary value problem
    Zhang, Keyu
    Sun, Qian
    O'Regan, Donal
    Xu, Jiafa
    AIMS MATHEMATICS, 2024, 9 (05): : 10911 - 10925
  • [50] On a System of Riemann-Liouville Fractional Boundary Value Problems with ρ-Laplacian Operators and Positive Parameters
    Henderson, Johnny
    Luca, Rodica
    Tudorache, Alexandru
    FRACTAL AND FRACTIONAL, 2022, 6 (06)
12345