Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Abstract

This paper contains modeling of a fuzzy-fractional financial chaotic model based on triangular fuzzy numbers (TFNs) to predict the idea that long-term dependency and uncertainty both have an impact on the financial market. For solution purposes, the He–Mohand algorithm is proposed where homotopy perturbation is hybrid with Mohand transform in a fuzzy-Caputo sense. In analysis, solutions and corresponding errors at upper and lower bounds are estimated. The obtained numerical results are displayed in tables to show the reliability and efficiency of the proposed methodology. Upper bound errors range from ${10}^{-6}$ to ${10}^{-12}$ and lower bound errors from ${10}^{-6}$ to ${10}^{-11}$ . For graphical analysis, system profiles are illustrated as two-dimensional and three-dimensional plots at diverse values of fractional parameters and time to comprehend the physical behavior of the proposed fuzzy-fractional model. These plots demonstrate that the interest rate, price index, and investment demand decrease with the increase of the value of the $\mathbb{r}$ -cut at the lower bound. At the upper bound, this behavior is totally opposite. The chaotic behavior of the system at smaller values of saving rate, elasticity of demands, and per-investment cost is greater in contrast to their larger value. Analysis reveals that the proposed methodology (He–Mohand algorithm) provides a new way of understanding the complicated structure of financial systems and provides new insights into the dynamics of financial markets. This algorithm has potential applications in risk management, portfolio optimization, and trading strategies.