Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative

• Published in: Journal of engineering mathematics Vol. 144; no. 1
• Main Authors: Alzahrani, Abdulrahman B. M., Saadeh, Rania, Abdoon, Mohamed A., Elbadri, Mohamed, Berir, Mohammed, Qazza, Ahmad
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Circuits; Complex systems; Computational Mathematics and Numerical Analysis; Decomposition; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Numerical methods; Robustness (mathematics); Runge-Kutta method; Theoretical and Applied Mechanics; Chaos; The Atangana–Baleanu fractional derivative; Numerical solution; Laplace decomposition method
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-023-10319-x

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.