Positive solutions for boundary value problem of Nonlinear fractional differential equation

We are concerned with the existence and nonexistence of positive solutions for the non-linear fractional boundary value problem: D-0+(alpha) u( t) +lambda a(t) f (u(t)) = 0, 0 < t < 1, u(0) = u'(0) = u'(1) = 0, where 2 < alpha < 3 is a real number and D-0+(alpha) 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. Copyright (c) 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.