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In this paper, we study the existence and uniqueness of solutions for the boundary value problem of fractional difference equations {equation presented} respectively, where {equation presented} is a continuous function and g ∈ C([ν - 3, ν + b]Zν-3,R) is a continuous functional. We prove the existence and uniqueness of a solution to the first problem by the contraction mapping theorem and the Brouwer theorem. Moreover, we present the existence and nonexistence of a solution to the second problem in terms of the parameter λ by the properties of the Green function and the Guo-Krasnosel'skii theorem. Finally, we present some examples to illustrate the main results. © 2013 Pan et al.; licensee Springer.

The existence of solutions to a class of boundary value problems with fractional difference equations