一类带有分数阶微分边值条件的分数阶微分方程在奇异的和非奇异的情况下的唯一正解(英文)

Unique Positive Solutions for a Class of Singular and Nonsingular Fractional Differential Equations with Fractional Derivative Boundary Value Conditions

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.

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.