Analysis of Noise on Ordinary and Fractional-Order Financial Systems - Hunida Malaikah; Jawaher Faisal Alabdali (Fractal and Fractional)
This study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random disturbances, whereas the fractional-order counterpart models memory-dependent behaviors by incorporating fractional Gaussian noise (FGN) characterized by a Hurst parameter that governs long-term correlations. This study used data generated through MATLAB simulations based on standard financial models from the literature. Numerical simulations compared system behavior in deterministic and noisy environments. The results reveal that ordinary systems experience transient fluctuations, quickly returning to a stable state, whereas fractional systems exhibit persistent deviations due to historical dependencies. This highlights the fundamental difference between integer-order and fractional-order derivatives in financial modeling. Our key findings indicate that noise significantly impacts interest rates, investment needs, price indices, and profit margins, with the fractional system displaying higher sensitivity to external shocks. These insights emphasize the necessity of incorporating memory effects in financial modeling to improve accuracy in predicting market behavior. The study further underscores the importance of adaptive monetary policies and risk management strategies to mitigate financial instability. Future research should explore hybrid models combining short-term stability with long-term memory effects for enhanced financial forecasting and stability analysis.