吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
JOURNAL OF JILIN UNIVERSITY(SCIENCE EDITION)
2014年
3期
482-488
,共7页
智二涛%刘锡平%李凡凡
智二濤%劉錫平%李凡凡
지이도%류석평%리범범
正解%Caputo导数%分数阶脉冲微分方程%不动点定理
正解%Caputo導數%分數階脈遲微分方程%不動點定理
정해%Caputo도수%분수계맥충미분방정%불동점정리
positive solutions%Caputo derivative%fractional impulsive differential equation%fixed point theorem
用非线性泛函分析理论研究分数阶脉冲微分方程边值问题，借助范数形式的锥拉伸-压缩不动点定理，证明了一类具有 Caputo 分数导数的脉冲微分方程边值问题正解的存在性，得到了正解存在的充分条件及相应的推论。
用非線性汎函分析理論研究分數階脈遲微分方程邊值問題，藉助範數形式的錐拉伸-壓縮不動點定理，證明瞭一類具有 Caputo 分數導數的脈遲微分方程邊值問題正解的存在性，得到瞭正解存在的充分條件及相應的推論。
용비선성범함분석이론연구분수계맥충미분방정변치문제，차조범수형식적추랍신-압축불동점정리，증명료일류구유 Caputo 분수도수적맥충미분방정변치문제정해적존재성，득도료정해존재적충분조건급상응적추론。
The boundary value problem of the fractional impulsive differential equation was studied by means of the nonlinear functional theory.Some existence theorems of positive solutions for the boundary value problem of fractional impulsive differential equation with Caputo derivative were proved with the help of the fixed point theorem of cone expansion and compression of norm type, obtaining the sufficient conditions about the existence of positive solutions and the relevant corollary.
