分数阶微分方程边值问题解的存在性(英文)  

Existence of Solutions to Boundary Value Problem for Fractional Differential Equations

作　　者：周文学[1,2] 彭济根[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：《工程数学学报》2011年第6期727-735,共9页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(10901075);the Key Project of Chinese Ministry of Education(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.本文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Carathéodory条件,利用非紧性测度的性质和Mnch’s不动点定理证明解的存在性.By means of the Green 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 the boundary value problem of nonlinear fractional differential equations. This article investigates the boundary value problem of nonlinear fractional differential equation. By applying Carathéodory conditions on the nonlinear terms, we obtain an existence result for the solution. Our analysis relies on the measure of noncompactness, the Mnch fixed point theorem and the reduction of the considered problem to its equivalent integral equation.

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

分 类 号：O175.8[理学—数学]