The existence and uniqueness of solutions to boundary value problems of fractional difference equations

被引：21
作者：
Yuanyuan Pan
Zhenlai Han
Shurong Sun
Zhiqing Huang
机构：
[1] School of Mathematical Sciences, University of Jinan, Shandong
来源：
Mathematical Sciences | 2012年 / 6卷 / 1期
基金：
中国国家自然科学基金;
关键词：
34B18; Boundary value problem; Brouwer theorem; Contraction mapping theorem; Discrete fractional equation; Existence and uniqueness of solution; Mathematics Subject Classification: 2010: 34A08;
D O I：
10.1186/2251-7456-6-7
中图分类号：
学科分类号：
摘要：
In this paper, we study the existence and uniqueness of solutions for the boundary value problem−Δν−μνy(t)=f(t,y(t+ν−1)),Δiy(ν−N)=0,i∈{0,…,N−3},ΔN−2y(ν−N)=g(y),Δν−Nμy(b+M+ν−μ)=0, whereν≥ 2 , 1 ≤ μ< ν, f: { 0 , · · · , b+ M} × R→ R is continuous, and nonnegative fory≥ 0 , g: C([ ν− N, · · · , b+ M+ ν] , R) is a given function. We give a representation for the solution to this problem, and we prove the existence and uniqueness of solution to this problem by contraction mapping theorem and Brouwer theorem. © 2012, Pan et al.; licensee Springer.
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