分数阶微分方程边值问题解的存在性  

Existence of Solution to Boundary Value Problem for Fractional Differential Equation

作　　者：周文学[1,2] 刘海忠[2] 

机构地区：[1]西安交通大学理学院,陕西西安710049 [2]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《兰州交通大学学报》2012年第1期157-162,共6页Journal of Lanzhou Jiaotong University

摘　　要：讨论了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Monch'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.By applying Caratheodory conditions to the nonlinear terms,we obtain an existence result for solution.Our analysis relies on the concept of measures of noncompactness and Monch＇s fixed point theorem.

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

分 类 号：O175.8[理学—数学]