具有线性微分算子的分数阶微分方程积分边值问题  

The integral boundary value problem for fractional differential equations with linear differential operator

作　　者：李萌萌[1] 贾梅[1] 苏小凤[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《纯粹数学与应用数学》2016年第1期75-83,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11171220);沪江基金(B14005)

摘　　要：研究一类具有分数阶线性微分算子的非线性微分方程积分边值问题解的存在性与唯一性.利用Schauder不动点定理及压缩映射原理,建立并证明了边值问题解的存在性定理和唯一性定理,并给出两个例子以说明所得结论.In this paper, we study the existence and uniqueness of solutions for a class of integral boundary value problem of differential equation with fractional linear differential operator. By using Schauder fixed point theorem and Banach contraction principle, the theorems of the existence and the uniqueness of solutions for the boundary value problem are obtained and proved. And we give two examples to illustrate the results.

关 键 词：分数阶线性微分算子 积分边值问题 Riemann-Liouville分数阶导数 不动点定理 

分 类 号：O175.8[理学—数学]