Boundary value problems for fractional difference equations with three-point fractional sum boundary conditions

Advances in Difference Equations

Sotiris K Ntouyas¹  Thanin Sitthiwirattham¹  Jessada Tariboon³ 

[1] Department of Mathematics, Faculty of Applied Science, King Mongkut’Department of Mathematics, University of Ioannina, Ioannina, Greece;s University of Technology, North Bangkok, Thailand

关键词: fractional difference equations;    boundary value problem;    existence;    uniqueness;    fixed point theorems;   

DOI  :  10.1186/1687-1847-2013-296

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a discrete fractional boundary value problem of the form{Δαx(t)=f(t+α−1,x(t+α−1)),t∈[0,T]N0:={0,1,…,T},x(α−2)=0,x(α+T)=Δ−βx(η+β),where1<α≤2,β>0,η∈Nα−2,α+T−1:={α−2,α−1,…,α+T−2,α+T−1}andf:[α−1,…,α+T−1]Nα−1×R→Ris a continuous function. Existence and uniqueness of the solutions are proved by using the contraction mapping theorem, the nonlinear contraction theorem and Schaefer’s fixed point theorem. Some illustrative examples are also presented. MSC:34A08, 26A33.

【 授权许可】

CC BY