This paper presents a novel numerical method for analvwing chaotic systems, focusing on applications to real-world problems. The Caputo-Fabrizio operator, a fractional derivative without a singular kernel, is used to investigate chaotic behavior. A fractional-order chaotic model is analvwed using numerical solutions derived from this operator, which captures the complexity of chaotic dynamics. In this paper, the uniqueness and boundedness of the solution are established using fixed-point theory. Due to the non-linearity of the system, an appropriate numerical scheme is developed. We further explore the model?s dynamical properties through phase portraits, Lyapunov exponents, and bifurcation diagrams. These tools allow us to observe the system???s sensitivity to varying parameters and derivative orders. Ultimately, this work extends the application of fractional calculus to chaotic systems and provides a robust methodology for obtaining insights into complex behaviors.