Electron. J. Diff. Equ., Vol. 2013 (2013), No. 29, pp. 1-5.

Existence of positive solutions for a nonlinear fractional differential equation

Habib Maagli

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.

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Habib Maagli
King Abdulaziz University, College of Sciences ant Arts
Rabigh Campus, Department of Mathematics
P.O. Box 344, Rabigh 21911, Kingdom of Saudi Arabia
email: habib.maagli@fst.rnu.tn

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