带有非局部条件Caputo分数阶差分方程解的存在性

Existence and Uniqueness of Solutions about Caputo Fractional Difference Equation with Nonlocal Conditions

考虑如下Caputo分数阶差分方程△νCy(t)=-(ft+ν-1,y(t+ν-1))在非局部条件y(ν-3)=φ(y),△y(ν+b)=ψ(y),△2y(ν-3)=λ(y)下的边值问题(BVP),其中t∈[0,b],f:[ν-2,ν-1,…,ν+b]Nν-2×R→R,f为连续函数,φ,ψ,λ∈C([ν-3,ν+b])→R,2<ν燮3。利用Banach压缩映射定理和Brouwer不动点定理得到此边值问题解存在的充分条件。

In this paper, we investigate the existence and uniqueness of solutions for fractional difference equation boundary value problem （BVP）：△C^v y（t）=-f（t＋v-1,y（t＋v-1）） y（v-3）=φ（y）,△y（v＋6）=ψ（y）,△^2y（v-3）=λ（y）,wheret∈[0,b],f：[v-2,v-1,…,v＋b]Nv-2×R→R, is continuous, φ,ψ,λ∈C（[v-3,v＋b]）→R,2〈v≤3. We use the Banach＇s contraction mapping principle to deduce the uniqueness theorem. By means of the Brouwer＇s fixed points theorem, we obtain sufficient condition for the existence of solution to boundary value problem.