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

Existence of positive solutions for a nonlinear fractional differential equation

Habib Maagli

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.

Show me the PDF file (178 KB), TEX file, and other files for this article.

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

Return to the EJDE web page