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

In this paper, we investigate the nonlinear differential equation of fractional order. C D 0 + α u ( t ) = f ( t , u ( t ) , u ′ ( t ) ) , 1 < α ⩽ 2 , 0 < t < 1 , where C D 0 + α is the Caputo fractional derivative, subject to the boundary conditions. u ( 0 ) + u ′ ( 0 ) = 0 , u ( 1 ) + u ′ ( 1 ) = 0 . ns of Schauder’s fixed point theorem and an extension of Krasnoselskii’s fixed point theorem in a cone, some results on the existence of positive solutions are obtained.