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

Abstract In this paper, we are concerned with the nonlinear differential equation of fractional order D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 t 1 , 1 α ≤ 2 , where D 0 + α is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions u ( 0 ) = 0 , D 0 + β u ( 1 ) = a D 0 + β u ( ξ ) . We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.