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 0Cu.t/ C f .t; u.t// D 0; 0 < t < 1; 1 < 2; where D 0C is the standard Riemann Liouville fractional order derivative, subject to the boundary conditions u.0/ D 0; D 0Cu.1/ D aD 0Cu. /: We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.