一类Caputo分数阶微分方程边值问题正解的存在性  

The Existence of Positive Solutions to a Class of Caputo Fractional Differential Equation Boundary Value Problem

作　　者：许丽[1] 翟成波[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《中北大学学报（自然科学版）》2013年第5期551-554,共4页Journal of North University of China(Natural Science Edition)

基　　金：国家青年科学基金资助项目(11201272);山西省青年科学基金资助项目(2010021002-1)

摘　　要：利用Krasnoselskii关于算子相加的不动点定理及格林函数的性质,研究了一类Caputo分数阶微分方程边值问题.通过先定义函数空间及空间中的紧算子和压缩映射,获得算子方程的不动点.进而给出了这类Caputo分数阶微分方程边值问题正解的存在性.By using Krasnoselskii fixed point theorem of sum operators and the properties of the Green function, a class of Caputo fractional differential equation boundary value problem was studied. First, by defining a function space with a compact operator and a contraction map on the space, the existence of fixed points for the operator equation was obtained. Further, the existence of positive solutions to the Caputo fractional differential equation boundary value problem was established.

关 键 词：Caputo分数阶微分方程 正解 存在性 KRASNOSELSKII不动点定理 

分 类 号：O175.8[理学—数学]