工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2012年
2期
299-308
,共10页
初值问题%分数阶微分方程%Caputo分数阶导数%非紧性测度%Carathéodory条件
初值問題%分數階微分方程%Caputo分數階導數%非緊性測度%Carathéodory條件
초치문제%분수계미분방정%Caputo분수계도수%비긴성측도%Carathéodory조건
initial value problem%fractional differential equations%Caputo fractional derivative%measure of noncompactness%Carathéodory condition
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.本文讨论菲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Carathéodory条件,利用非紧性测度的性质和M(o)nch,8不动点定理证明解的存在性.
利用Green函數可以將分數階微分方程初值問題轉化為等價的積分方程.近來此方法被應用于討論非線性分數階微分方程初值問題解的存在性.本文討論菲線性分數階脈遲微分方程初值問題,應用Green函數,將其轉化為等價的積分方程,併設非線性項滿足Carathéodory條件,利用非緊性測度的性質和M(o)nch,8不動點定理證明解的存在性.
이용Green함수가이장분수계미분방정초치문제전화위등개적적분방정.근래차방법피응용우토론비선성분수계미분방정초치문제해적존재성.본문토론비선성분수계맥충미분방정초치문제,응용Green함수,장기전화위등개적적분방정,병설비선성항만족Carathéodory조건,이용비긴성측도적성질화M(o)nch,8불동점정리증명해적존재성.
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 Carathéodory conditions on the nonlinear terms,we obtain an existence result for solution.Our analysis relies on the concept of measures of noncompactness and M(o)nch's fixed point theorem and the reduction of the considered problem to the equivalent of integral equations.
