Abstract In this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

中文翻译：

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非自治狄利克雷分数离散问题的非平凡解

摘要 在本文中，我们介绍了具有微扰项的有限分数阶差分方程的两点边值问题。通过应用谱理论，将关联的格林函数构造为一系列函数并获得其一些性质。在方程非线性部分的合适条件下，推导出了一些存在唯一性的结果。