The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer order ώ ∈ (1, 2]. The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder’s fixed point theorem for existence. Also, we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable. Example for the illustration of results is given.

中文翻译：

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具有多点求和边界条件的非线性分数阶差分方程的 Ulam-Hyers-Rassias 稳定性和解的存在性

本研究的目的是获得一些条件，揭示了一类非整数阶 ώ ∈ (1, 2] 的差分方程解的存在性和稳定性。所需条件是通过应用唯一性收缩原理的技术获得的和 Schauder 不动点定理的存在性。此外，我们建立了所考虑的一类差分方程的解是广义 Ulam-Hyers-Rassias 稳定的一些条件，并给出了结果说明的例子。