Existence and uniqueness of a positive solution to singular fractional differential equations

被引：18

作者：

Wang, Yongqing ^{[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 Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

BOUNDARY VALUE PROBLEMS | 2012年

基金：

中国国家自然科学基金;

关键词：

fractional differential equation; positive solution; iterative scheme; singular boundary value problem; BOUNDARY-VALUE-PROBLEMS;

D O I：

10.1186/1687-2770-2012-81

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the existence and uniqueness of a positive solution to the following singular fractional differential equation with nonlocal boundary value conditions: {D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, D(0+)(beta)u(1) = Sigma(m-2)(i=1) eta(i)D(0+)(beta)u(xi(i)), where 1 < alpha <= 2, 0 < beta < alpha - 1, 0 < xi(1) < ... < xi(m-2) < 1 with Sigma(m-2)(i=1) eta(i)xi(alpha-beta-1)(i) < 1, D-0+(alpha) is the standard Riemann-Liouville derivative, f may be singular at t = 0, t = 1, u = 0.

引用

页数：12

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