分数阶脉冲微分方程初值问题解的存在性(英文)  

Existence of Solution to IVP for Impulsive 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]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》2012年第2期299-308,共10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：利用Green函数可以将分数阶微分方程初值问题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初值问题解的存在性.本文讨论非线性分数阶脉冲微分方程初值问题,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Carath′eodory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 the means of the Green’s function,the initial 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 initial value problem of nonlinear fractional differential equation.This article investigates the initial value problem of nonlinear impulsive fractional differential equation.By applying Carath′eodory conditions on the nonlinear terms,we obtain an existence result for solution.Our analysis relies on the concept of measures of noncompactness and Mnch’s fixed point theorem and the reduction of the considered problem to the equivalent of integral equations.

关 键 词：初值问题 分数阶微分方程 CAPUTO分数阶导数 非紧性测度 Carath′eodory条件 

分 类 号：O175.8[理学—数学]