Positive solutions for mixed problems of singular fractional differential equations

被引：76

作者：

Agarwal, Ravi P. ^{[1
]}

O'Regan, Donal ^{[2
]}

Stanek, Svatoslav ^{[3
]}

机构：

[1] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

[2] Natl Univ Ireland, Dept Math, Galway, Ireland

[3] Palacky Univ, Dept Math Anal, Fac Sci, Olomouc 77146, Czech Republic

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 01期

关键词：

Fractional differential equation; Caputo fractional derivative; singular mixed problem; positive solution; regularization; fixed point theorem on cones; MSC (2010) 26A33; 34B16; BOUNDARY-VALUE PROBLEM;

D O I：

10.1002/mana.201000043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence of positive solutions to the singular fractional boundary value problem: D-c(a) u + f(t, u, u', D-c(mu) u) = 0, u'(0) = 0, u(1) = 0, where 1 < alpha < 2, 0 < mu < 1, f is a L-q-Caratheodory function, q > 1/a 1, and f( t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here D-c stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：27 / 41

页数：15

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