The Impact of White Noise on Chaotic Behavior in a Financial Fractional System with Constant and VariableOrder: A Comparative Study

In this study, we investigated the impact of white noise on the chaotic dynamics of a financial system with Caputo fractional derivatives of constant- and variable-order. We solve thesefractional financial systems numerically. We analyze the chaotic behavior of these fractional-order hyperchaotic systems through simulations, study the effects of white noise on chaotic dynamics, and provide a comparison between fractional hyperchaotic systems of constant and variable orders. The study reveals that white noise can either amplify or suppress chaos, with significant differences observed between the constant- and variable-order cases. We obtained numerous intriguing graphical findings for the model by evaluating various scenarios. The findings provide useful information for better understanding financial market dynamics in the presence of noise.