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中文摘要：
本文研究下列分数阶微分方程在奇异和非奇异的情况下的边值问题{D_0~α＋u（t）＋f（t,u（t））=0,t∈（0,1）,3〈α≤4,u（0）=0,D_（0＋）~（α-1）u（0）=0,D_（0＋）~（α-2）u（0）=0,D_（0＋）~（a-3）u（1）=0.通过计算,得到分数阶格林公式.利用半序集上的不动点定理和u_0凸算子不动点定理,得到上述问题存在唯一正解.
英文摘要：
In this paper,we consider the following singular and nonsingular fractional differential equation boundary value problem{D_0~α＋u（t）＋f（t,u（t））=0,t∈（0,1）,3α≤4,u（0）=0,D_（0＋）~（α-1）u（0）=0,D_（0＋）~（α-2）u（0）=0,D_（0＋）~（a-3）u（1）=0.By calculating,we obtain the fractional Green function.By using a fixed point theorem in partially ordered sets and a fixed point theory for the u_0 concave operator,some results on the existence and uniqueness of positive solutions can be established.
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