摘要：In this paper, we consider a discrete fractional boundary value problem of the form { Δ α x ( t ) = f ( t + α − 1 , x ( t + α − 1 ) ) , t ∈ [ 0 , T ] N 0 : = { 0 , 1 , … , T } , x ( α − 2 ) = 0 , x ( α + T ) = Δ − β x ( η + β ) , where 1 0 , η ∈ N α − 2 , α + T − 1 : = { α − 2 , α − 1 , … , α + T − 2 , α + T − 1 } and f : [ α − 1 , … , α + T − 1 ] N α − 1 × R → R is 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.
关键词：fractional difference equations ; boundary value problem ; existence ; uniqueness ; fixed point theorems
