带有非局部条件分数阶差分方程解的存在性和唯一性

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

主要考虑如下分数阶差分方程△^vy（t）=-f（t＋v-1,y（t＋v-1））在非局部条件y（v-2）=ψ（y）,y（v＋b）=ψ（y）下的边值问题（BVP）,其中t∈[0,b],f：[v-1,v,…,v＋b-1]_（N_（v-1））×R→R,f为连续函数,（？）,ψ∈C（v-2,v＋b]）→R。

In this paper, we investigate the existence and uniqueness of solutions for frac- tional difference equation boundary value problem（BVP）：△^vy（t）=-f（t＋v-1,y（t＋v-1））y（v-2）=ψ（y）,y（v＋b）=ψ（y）where t∈[0,b],f：[v-1,v,…,v＋b-1]_（N_（v-1））×R→[0,＋∞] is continuous, Ф, ψ ∈C（[v- 2, v ＋ b]） →R, 1 〈 v ≤ 2. We use the Banach＇s contraction mapping principle todeduce 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.