含积分边值条件的非线性分数阶微分方程解的存在性与唯一性

Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions

研究了一类含积分边值条件的非线性分数阶微分方程{~cD~αu(t)+f(t,u(t))=0,t∈[0,1],u(0)=u″(0)=0,u(1)=λ∫10u(s)ds解的存在性和唯一性.利用不动点定理,得到了该边值问题解的存在性与唯一性定理.作为主要结论的应用,给出2个例子验证了所得结果.

The following nonlinear fractional differential equations with integral boundary value conditions as the form of {^cD^αu（t）＋f（t,u（t））=0,t∈[0,1],u（0）=u″（0）=0,u（1）=λ∫0^1u（s）ds is studied. The theorems of the existence and uniqueness of positive solutions are obtained and proved by using the fixed point theorem and Banach contraction mapping principle. As an application, two examples are given to illustrate the main results.