In this paper, we prove existence of solutions for an eigenvalue problem in the fractional h-discrete calculus. Dirichlet type boundary conditions are considered. Several properties for Green’s function of the associated problem are proven. A fixed point theorem in Cone theory is a main tool to obtain sufficient conditions on upper and lower bounds for eigenvalues of the boundary value problem so that the existence of positive solutions are guaranteed.

中文翻译：

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分数阶h离散微积分中的一个特征值问题

在本文中，我们证明了分数h离散微积分中特征值问题的解的存在性。考虑狄利克雷型边界条件。证明了相关问题的格林函数的几个性质。圆锥理论中的不动点定理是获得边值问题特征值上下界的充分条件以保证正解存在的主要工具。