Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 29, pp. 1-5.

Title: Existence of positive solutions for a nonlinear fractional 
       differential equation
        
Author: Habib Maagli (King Abdulaziz Univ., Rabigh, Saudi Arabia)
        
Abstract:
 Using the Schauder fixed point theorem, we prove an existence of
 positive solutions for the  fractional differential problem
 in the half line $\mathbb{R}^+=(0,\infty)$:
 $$
 D^{\alpha}u=f(x,u),\quad \lim_{x \to 0^+}u(x)=0,
 $$
 where $\alpha \in (1,2]$ and $f$ is a Borel measurable function
 in $\mathbb{R}^+\times \mathbb{R}^+$ satisfying some appropriate
 conditions.

Submitted November 25, 2012. Published January 28, 2013.
Math Subject Classifications: 34A08.
Key Words: Riemann-Liouville fractional derivative; fixed point theorem.