Chaos and forecasting financial risk dynamics with different stochastic economic factors by using fractional operator

In this paper, we developed a new fractional order nonlinear model for dynamics and forecasting of economic diversification with different stochastic engineering factors serve a crucial role in promoting socio-economic progress. Boundedness, positivity, and unique solutions at equilibrium points are used in the qualitative and quantitative study of a proposed model with the Banachs contraction theorem, Schauders fixed-point theorem, and fixed-point theory. Ulam–Hyers–Rassias stability establishes the stability criteria of the caputo fractional order developed model. We employed method of moment quintile regression to validate the coefficient parameters of the compartments for forecasting and modeling. Theoretical predictions are validated using the two-step Newton Polynomial Method, and numerical results, showing a high degree of agreement between the theoretical analysis and the numerical results. The results indicate that tourism, green finance, and foreign direct investment play a pivotal role in driving economic growth and have social are shown in phase patriots simulation results bounded in feasible domain. According to our research, in order to divorce economic growth from environmental stressors, leading tourist nations should increase green finance, expand in the tourism sector, and draw in foreign direct investment.