Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

• Published in: Advances in continuous and discrete models 2024-01, Vol.2024 (1), p.5, Article 5
• Main Author: Zhao, Kaihong
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis; Boundary value problems; Computer simulation; Difference and Functional Equations; Fixed points (mathematics); Functional Analysis; Laplace transforms; Mathematics; Mathematics and Statistics; Metric space; Nonlinear analysis; Numerical methods; Ordinary Differential Equations; Partial Differential Equations; Simulation; Stability analysis; Systems stability
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-024-03801-y

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.