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.