Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
复制标题
DOI：
10.1016/j.camwa.2010.10.041
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
C. Goodrich
中科院分区：
文献类型：
--
作者：
C. Goodrich
本文考虑形式为−Δνy(T)=f(t+ν−1，y(t+ν−1))，y(ν−2)=g(Y)，y(ν+b)=0的离散分数阶边值问题，其中[公式：见文本]是连续的，[公式：见文本]是给定的泛函，1<；ν≤2.我们给出了这个问题的解的表示.最后，我们利用非线性泛函分析中的各种工具，包括压缩映象定理、Brouwer定理和Krasnosel‘skii定理，证明了该问题解的存在唯一性。
In this paper, we consider a discrete fractional boundary value problem of the form −Δνy(t)=f(t+ν−1,y(t+ν−1)), y(ν−2)=g(y), y(ν+b)=0, where [Formula: see text] is continuous, [Formula: see text] is a given functional, and 1<ν≤2. We give a representation for the solution to this problem. Finally, we prove the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel’skii theorem.