一类含积分边界条件分数阶微分方程解的存在性和唯一性

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

研究一类含积分边界条件非线性分数阶微分方程{~CD~αu(t)+f(t,u(t))=0,2<α<3,0<t<1, u(0)=u″(0)=0,u(1)=λ∫10u(s)ds,0<λ<2,解的存在性和唯一性,借助于Green函数的性质,利用Schauder不动点定理和Banach压缩映射原理,得到该边值问题解的存在性和唯一性定理,并举例验证所得结论的有效性.

In this paper, we studied the following nonlinear fractional differential equations with integral boundary value conditions as the form of {CD^αu（t）＋f（t,u（t））=0,0〈t〈1,n〈α〈n＋1,n≥2（n∈N）,u（0）=u′0）=…=u^（n-2）（0）=u^（n）（0）=0,u（1）=λ∫0^1u（s）ds,0〈λ〈2,The theorems of the existence and uniqueness were obtained by using the properties of the associated Green＇s function Schauder, fixed point theorem and banach contraction mapping principle. Three examples were given to illustrate the advantages of the obtained results.