APPLICATION OF FRACTAL-FRACTIONAL OPERATORS TO FRACTIONAL CHAOTIC SYSTEMS: INSIGHTS INTO COMPLEX DYNAMICS

This study investigates the chaotic dynamics of the fractional Lorenz–Lü–Chen system using fractal-fractional operators with the Liouville–Caputo kernel. A variational iteration method is applied to construct approximate analytical solutions, and Lyapunov exponents are used to confirm chaos. Numerical simulations demonstrate how varying fractional orders influence system behavior. The results highlight the potential of fractal-fractional modeling in capturing memory effects and long-range interactions, offering new insights for controlling chaotic systems in physical applications such as hydraulic oscillators.