Chaotic Dynamics and Numerical Solutions of the Stochastic Fractional-Order Lorenz System

Objectives This study proposes a novel numerical scheme for solving a new class of chaotic systems, with particular focus on the stochastic fractional-order Lorenz system (SFLS). The objective is to enhance the modeling and analysis of SFLS under a fractional framework while investigating the dynamical effects of multiplicative white noise. Materials and Methods The SFLS is formulated using the Atangana–Baleanu–Caputo fractional derivative. A robust numerical algorithm is developed to obtain approximate solutions of the system in the presence of multiplicative white noise. The performance and validity of the proposed method are demonstrated through comprehensive two-dimensional (2D) and three-dimensional (3D) numerical simulations. Results The computational results confirm that the proposed scheme accurately captures the stochastic and chaotic dynamics of the fractional-order Lorenz system. The simulations illustrate the significant influence of multiplicative white noise on system trajectories and stability characteristics. The method exhibits reliability, stability, and computational efficiency in approximating the system’s behavior. Conclusion The proposed numerical framework provides an effective tool for analyzing stochastic fractional chaotic systems. The findings contribute to improved modeling and prediction of noise-driven chaotic phenomena, with potential applications in climate and weather modeling, engineering systems, and economic forecasting where stochastic perturbations play a critical role.