A novel numerical method for stochastic conformable fractional differential systems

Abstract

This study introduced the conformable fractional discrete Temimi–Ansari method (CFDTAM), a novel numerical framework designed to solve fractional stochastic nonlinear differential equations with enhanced efficiency and accuracy. By leveraging the conformable fractional derivative (CFD), the CFDTAM unifies classical and fractional-order systems while maintaining computational simplicity. The method's efficacy was demonstrated through applications to a stochastic population model and the Brusselator system, showcasing its ability to handle nonlinear dynamics with high precision. A comprehensive convergence analysis was also conducted to validate the reliability and stability of the proposed method. All computations were performed using Mathematica 12 software, ensuring accuracy and consistency in numerical simulations. CFDTAM sets a new benchmark in fractional stochastic modeling, paving the way for advancements in partial differential equations, delay systems, and hybrid models.