中文摘要：

考虑有序Banach空间E中分数阶微分方程边值问题{-D0^a＋u（t）=f（t,u（t）,u（t））,t∈I,u（0）=u（1）=θ解的存在性，其中1〈a≤2是实数，j—Eo，1]，D；＋是标准的Riemann—Liouville导数，fEC（IXEXE，E）．将L-拟上下解对的概念引入非线性分数阶微分方程，在较弱的单调性条件和非紧性测度条件下，通过构造L．拟上下解对的混合单调过程，获得该边值问题最小、最大L拟解对的存在性及解的存在唯一性．

英文摘要：

The existence of solutions for the boundary value problems of the fractional differential equation in an ordered Banach space E,{-D0^a＋u（t）=f（t,u（t）,u（t））,t∈I,u（0）=u（1）=θis considered, where 1≤α≤2 is real number, I=[0,1], D;＋ is the standard Riemann-Liouville fractional derivative, f∈C（IX E）〈 E,E）. The concept of L-quasi-upper and lower solutions is introduced for the boundary value problem of nonlinear fractional equations. Under more general conditions of monotonicity and noncompactness measure, by using the monotone iteration scheme with L-quasi-upper and lower solutions, the minimum and maximum L-quasi-solutions of the problems are derived and the existence of solution for the problems between them is shown.