分数阶微分方程边值问题解的存在性  

Existence of Solution to BVP for Fractional Differential Equation

作　　者：周文学[1,2] 

机构地区：[1]兰州交通大学数学系,兰州730070 [2]西安交通大学理学院,西安710049

出　　处：《应用泛函分析学报》2011年第4期405-412,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10901075);教育部科学技术研究重大项目(210226)

摘　　要：应用Green函数将分数阶微分方程边值问题可转化为等价的积分方程.近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性.讨论非线性分数阶微分方程边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项满足Caratheodory条件,利用非紧性测度的性质和M(o|¨)nch's不动点定理证明解的存在性.By the means of the Green＇s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation. Recently, this method is used successfully to discuss the existence of the solution to boundary value problem of nonlinear fractional differential equation. This article investigates the boundary value problem of nonlinear fractional differential equation. By applying Caratheodory conditions on the nonlinear terms, we obtain an existence result for solution. Our analysis relies on the concept of measures of noncompactness, MSnch＇s fixed point theorem and the reduction of the considered problem to the equivalent of integral equations.

关 键 词：边值问题 非紧性测度 Carathéodory条件 分数阶微分方程 CAPUTO分数阶导数 

分 类 号：O175.8[理学—数学] O177.91[理学—基础数学]