一类Caputo分数阶差分方程边值问题解的存在性

摘要

研究了一类Caputo分数阶差分方程边值问题解的存在性.利用Caputo分数阶差分方程及边值条件的特性给出了它的Green's函数,借助于Banach压缩映像原理、Krasnosel'skiis不动点定理和Leray-Schauder非线性抉择定理得到边值问题解的存在性,作为应用,给出一个例子验证所得的主要结果.%The existence of solution to boundary value problem of a class of Caputo fractional-order difference equations is studied.The features of these equations and boundary conditions are used to give out their Green's function.The existence of solutions to boundary value problem is obtained by means of Banach's contraction mapping principle,Krasnosel'skiis fixed point theorem,and Leray-Schauder nonlinear alternative theorem,and as an application,an example is given to verify the main result obtained.