Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations

In this paper, we are concerned with the nonlinear differential equation of fractional order D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, 1 < alpha <= 2, where D-0+(alpha) is the standard Riemann-Liouville fractional order derivative, subject to the boundary conditions u(0) = 0, D(0+)(beta)u(1) = aD(0+)(beta)u(xi). We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems. (C) 2009 Elsevier Ltd. All rights reserved.