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

页码：462 / 476

页数：15

共 50 条

[21] Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems
Henderson, Johnny
Luca, Rodica
Tudorache, Alexandru
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2016, 2016
[22] Nontrivial solutions for an integral boundary value problem involving Riemann-Liouville fractional derivatives
Fu, Zhengqing
Bai, Shikun
O'Regan, Donal
Xu, Jiafa
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)
[23] Positive Solutions for a High-Order Riemann-Liouville Type Fractional Integral Boundary Value Problem Involving Fractional Derivatives
Wang, Wuyang
Ye, Jun
Xu, Jiafa
O'Regan, Donal
SYMMETRY-BASEL, 2022, 14 (11):
[24] BOUNDARY-VALUE PROBLEMS FOR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL INCLUSIONS IN BANACH SPACES
Hamani, Samira
Henderson, Johnny
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[25] Existence of Positive Solutions to Boundary Value Problems with Mixed Riemann-Liouville and Quantum Fractional Derivatives
Nyamoradi, Nemat
Ntouyas, Sotiris K.
Tariboon, Jessada
FRACTAL AND FRACTIONAL, 2023, 7 (09)
[26] Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives
Qiu, Xiaowei
Xu, Jiafa
O'Regan, Donal
Cui, Yujun
JOURNAL OF FUNCTION SPACES, 2018, 2018
[27] Positive Solutions for a Semipositone Singular Riemann-Liouville Fractional Differential Problem
Agarwal, Ravi P.
Luca, Rodica
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2019, 20 (7-8) : 823 - 831
[28] Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem
Kopteva, Natalia
Stynes, Martin
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2017, 43 (01) : 77 - 99
[29] Solvability of a boundary value problem for a mixed-type equation with a partial Riemann-Liouville fractional derivative
Kilbas, A. A.
Repin, O. A.
DIFFERENTIAL EQUATIONS, 2010, 46 (10) : 1457 - 1464
[30] Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem
Natalia Kopteva
Martin Stynes
Advances in Computational Mathematics, 2017, 43 : 77 - 99

← 1 2 3 4 5 →