摘要：In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: − D 0 + α x ( t ) = f ( t , x ( t ) , x ( t ) ) + g ( t , x ( t ) ) $-D_{0+}^{\alpha}x(t)=f(t, x(t), x(t))+g(t, x(t))$ , 0 < t < 1 $0< t <1$ , 1 < α < 2 $1< \alpha<2$ , where D 0 + α $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, subject to either the boundary conditions x ( 0 ) = x ( 1 ) = 0 $x(0)=x(1)=0$ or x ( 0 ) = 0 $x(0)=0$ , x ( 1 ) = β x ( η ) $x(1)=\beta x(\eta)$ with η , β η α − 1 ∈ ( 0 , 1 ) $\eta, \beta\eta^{\alpha-1} \in(0,1)$ . We also construct an iterative scheme to approximate the solution. As applications of the main results, two examples are given.
关键词：fractional differential equation ; boundary value problem ; fixed point theorem ; mixed monotone operators
