Abstract and Applied Analysis
Volume 2007 (2007), Article ID 10368, 8 pages
doi:10.1155/2007/10368 

Positive solutions for boundary value problem of nonlinear fractional differential equation

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.