含积分边值条件的分数阶微分方程耦合系统正解的唯一性

Uniqueness of positive solution for a nonlinear fractional differential equation coupled system with integral boundary value condition

本文研究了一类含积分边值条件的非线性分数阶微分方程耦合系统{~cD~αu(t)+f(t,u(t),v(t))=0,~cD~αv(t)+f(t,u(βt),v(βt))=0,u(0)=u′(0)=…=u^(n-2)(0)=u^(n)(0)=0,u(1)=λ∫01u(s)ds,v(0)=v′(0)=…=v^(n-2)(0)=v^(n)(0)=0,v(1)=λ∫01v(s)ds正解的唯一性.利用广义耦合不动点定理,本文得到了该边值问题正解的唯一性的充分条件,并在举例说明了定理的有效性.

In this paper,we studied the uniqueness of positive solution for a fractional differential coupled system with integral boundary value condition as the form of {cDau（t）＋f（t,u（t）,v（t））=0,cDav（t）＋f（t,u（βt）,v（βt））=0,u（0）=u（0）=…=u（n-2）（0）=u（n）（0）=0,u（1）=λ∫1_0u（s）ds,v（0）=v（0）=…=v（n-2）（0）=v（n）（0）=0,v（1）=λ∫1_0v（s）ds Uniqueness of positive solution is obtained by using the generalized coupled fixed point. As an applica- tion, an example is given to illustrate our main result.