Abstract and Applied Analysis
Volume 2007 (2007), Article ID 10368, 8 pages
doi:10.1155/2007/10368
Research Article
Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation
Department of Mathematics, College of Education, College of Education, P.O. Box 3771, Unizah-Qasssim, Saudi Arabia
Received 16 May 2007; Revised 24 July 2007; Accepted 26 September 2007
Academic Editor: Ferhan Merdivenci Atici
Copyright © 2007 Moustafa El-Shahed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:
D0+αu(t)+λa(t) f(u(t))=0, 0<t<1,
u(0)=u′(0)=u′(1)=0,
where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.