In this paper, we consider a discrete-time fractional model of abstract form involving the Riemann-Liouville-like difference operator. On account of the C 0 -semigroups generated by a closed linear operator A and based on a distinguished class of sequences of operators, we show the existence of stable solutions for the nonlinear Cauchy problem by means of fixed point technique and the compact method. Moreover, we also establish the Ulam-Hyers-Rassias stability of the proposed problem. Two examples are presented to explain the main results.

中文翻译：

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离散时间抽象分数阶微分方程的稳定性分析

在本文中，我们考虑了涉及Riemann-Liouville型差分算子的抽象形式的离散时间分数模型。基于一个封闭的线性算子A生成的C 0-半群，并基于一类特殊的算子序列，我们通过不动点技术和紧致方法，证明了非线性柯西问题的稳定解的存在。此外，我们还建立了所提出问题的Ulam-Hyers-Rassias稳定性。给出两个例子来解释主要结果。