Positive solutions for Dirichlet problems, of singular nonlinear fractional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:371

Article

Agarwal, Ravi P.^1,2  O'Regan, Donal³  Stanek, Svatoslav⁴ 

[1] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

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

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

关键词: Fractional differential equation;    Singular Dirichlet problem;    Positive solution;    Riemann-Liouville fractional derivative;   

DOI  :  10.1016/j.jmaa.2010.04.034

来源: Elsevier

【 摘 要 】

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: D(alpha)u(t) + f (t, u(t), D-mu u(t)) = 0, u(0) = u(1) = 0, where 1 < alpha < 2, 0 < mu <= alpha - 1, D-alpha is the standard Riemann-Liouville fractional derivative, f is a positive Caratheodory function and f (t, x, y) is singular at x = 0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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