Numerical Simulation and Solutions for the Fractional Chen System via Newly Proposed Methods

This study presents two methods: a novel numerical scheme that utilizes the Atangana–Baleanu–Caputo (ABC) derivative and the Laplace New Iterative Method (LNIM). Furthermore, some complex dynamic behavior of fractional-order Chen is observed. The NABC method illustrates chaotic systems. We used the LNIM method to find analytical solutions for fractional Chen systems. The method stands out for its user-friendliness and numerical stability. The proposed methods are effective and yield analytical solutions and detection of chaotic behavior. Simultaneously, this results in a more precise understanding of the system. As a result, we may apply the approach to different systems and achieve more accurate findings. Furthermore, it has been demonstrated to be effective in accurately identifying instances through the exhibition of attractor chaos. Future applications in science and engineering can utilize these two methods to find numerical simulations and solutions to a variety of models.