We study a class of nonlinear fractional difference equations with nonlocal boundary conditions at resonance. The system is inspired by the three‐point boundary value problem for differential equations that have been extensively studied. It is also an extension to a fractional difference equation arising from real‐world applications. Converting the problem to an equivalent system corresponding to the integral operator and Green's function for differential equations, we are able to apply the coincidence degree theory for semilinear operators to obtain sufficient conditions for the existence of solutions. In addition, we prove a new property of the Gamma function and construct a family of examples to illustrate the applications of the results.

中文翻译：

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一类分数阶差分方程共振时解的存在性

我们研究了一类具有非局部边界条件的非线性分数阶差分方程。该系统的灵感来自已经广泛研究的微分方程的三点边值问题。它也是对实际应用中产生的分数差分方程的扩展。将问题转换为对应于积分算子和格林函数的微分方程的等价系统，我们能够将重合度理论应用于半线性算子，以获得解存在的充分条件。此外，我们证明了Gamma函数的新性质，并构建了一系列实例来说明结果的应用。