Effective Methods for Numerical Analysis of the Simplest Chaotic Circuit Model with Atangana–Baleanu Caputo Fractional Derivative

This paper comprehensively studies effective numerical methods for solving the simplest chaotic circuit model. We introduce a novel scheme for the Atangana–Baleanu Caputo fractional derivative (ABC-FD), coupled with the Laplace decomposition method (LDM). Furthermore, we rigorously compare the performance of these proposed methods with the Runge–Kutta fourth-order method. Using two mathematical techniques, we have discovered effective and highly convergent solutions to the chaotic model. We gave different values to the parameters to plot the chaos and create a phase portrait of the system. Therefore, the provided methods can be applied to more sophisticated examinations of different models. This study advances numerical techniques for understanding chaotic dynamics in complex systems. By introducing a novel scheme for the Atangana–Baleanu Caputo fractional derivative and the Laplace decomposition method, we provide a robust framework for effectively solving the simplest chaotic circuit model. This framework enhances accuracy and efficiency in unraveling chaotic behaviors, contributing to a broader understanding of chaotic dynamics across scientific domains in the future.