This paper investigates the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. The main contributions include: 1. **System Transformation**: The system is transformed into a nonimpulsive system to simplify the analysis. 2. **Existence and Uniqueness**: The existence and uniqueness of solutions are established using an F-contractive operator and a fixed-point theorem in a metric space. 3. **Generalized UH-Stability**: The generalized UH-stability is proven using nonlinear analysis methods. 4. **Numerical Simulation**: A novel numerical simulation algorithm is proposed. 5. **Illustrative Example**: An example is provided to validate the theoretical results and the effectiveness of the algorithm. The paper begins with an introduction to ABC-fractional derivatives and their applications, followed by a review of the $p$-Laplacian differential equation and its relevance in describing impulsive phenomena. The main system is defined as a nonlinear impulsive ABC-fractional coupled system with a $(p_1, p_2)$-Laplacian, incorporating both fractional derivatives and impulses. The authors then present the main results, including the existence and uniqueness of solutions, generalized UH-stability, and the proposed numerical simulation algorithm. Finally, an example is used to demonstrate the correctness and effectiveness of the theoretical findings.This paper investigates the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. The main contributions include: 1. **System Transformation**: The system is transformed into a nonimpulsive system to simplify the analysis. 2. **Existence and Uniqueness**: The existence and uniqueness of solutions are established using an F-contractive operator and a fixed-point theorem in a metric space. 3. **Generalized UH-Stability**: The generalized UH-stability is proven using nonlinear analysis methods. 4. **Numerical Simulation**: A novel numerical simulation algorithm is proposed. 5. **Illustrative Example**: An example is provided to validate the theoretical results and the effectiveness of the algorithm. The paper begins with an introduction to ABC-fractional derivatives and their applications, followed by a review of the $p$-Laplacian differential equation and its relevance in describing impulsive phenomena. The main system is defined as a nonlinear impulsive ABC-fractional coupled system with a $(p_1, p_2)$-Laplacian, incorporating both fractional derivatives and impulses. The authors then present the main results, including the existence and uniqueness of solutions, generalized UH-stability, and the proposed numerical simulation algorithm. Finally, an example is used to demonstrate the correctness and effectiveness of the theoretical findings.