中文摘要：

研究了阶数介于3到4之间的一类分数阶差分方程的边值问题。通过构造相应的Green函数，证明Green函数的正性性质，利用Banach压缩映像原理和Brouwer不动点定理，在合适的条件下，获得了边值问题解的存在唯一性。特别地，当阶数w=4时，原问题变为整数阶差分方程边值问题，研究结果表明，分数阶差分方程边值问题与整数阶差分方程边值问题具有本质区别。

英文摘要：

This paper is concerned with boundary value problems of fractional difference equations with the order between 3 to 4. Green function is technically constructed, the positivity of Green function is obtained. Under the suitable conditions, the existence and uniqueness of solutions of boundary value problems for fractional order difference equations with a parameter is proved by using of Banach contraction mapping principle and Brouwer fixed point theorem. In particular, the difference between fractional order difference equations and integer order difference equations is found, which is significant on research of fractional order difference equations.