In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive system by applying an appropriate transformation. Secondly, the existence and uniqueness of the solution are obtained by an F-contractive operator and a fixed-point theorem on metric space. Simultaneously, the generalized UH-stability is established based on nonlinear analysis methods. Thirdly, a novel numerical simulation algorithm is provided. Finally, an example is used to illustrate the correctness and availability of the main results. Our study is a beneficial exploration of the dynamic properties of viscoelastic turbulence problems.

在本文中，我们研究了具有拉普拉斯算子和脉冲的非线性 Atangana-Baleanu-Caputo (ABC) 分数耦合系统的可解性和广义 Ulam-Hyers (UH) 稳定性。首先，通过应用适当的变换，该系统成为非脉冲系统。其次，通过F-收缩算子和度量空间上的不动点定理得到解的存在唯一性。同时，基于非线性分析方法建立了广义UH稳定性。第三，提供了一种新颖的数值模拟算法。最后通过算例说明了主要结果的正确性和可用性。我们的研究是对粘弹性湍流问题的动态特性的有益探索。