The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

中文翻译：

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离散分数阶两点边值问题与一些相关的物理应用

本文报道的结果与离散分数阶两点边值问题解的存在性和唯一性有关。通过利用Caputo和Riemann-Liouville分数差分算子的性质，收缩映射原理和Brouwer不动点定理来开发结果。此外，建立了所提出的离散分数边值问题的Hyers-Ulam稳定性和Hyers-Ulam-Rassias稳定性的条件。理论结果的适用性已通过相关的实例得到了证明。所考虑的数学模型的分析用数字说明并以表格形式显示。比较结果并讨论重叠/不重叠的发生。