Abstract
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.
| Original language | English (Ireland) |
|---|---|
| Pages (from-to) | 57-68 |
| Number of pages | 12 |
| Journal | Journal Of Mathematical Analysis And Applications |
| Volume | 371 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Nov 2010 |
Keywords
- Fractional differential equation
- Positive solution
- Riemann-Liouville fractional derivative
- Singular Dirichlet problem
Authors (Note for portal: view the doc link for the full list of authors)
- Authors
- Agarwal, RP,O'Regan, D,Stanek, S