Stability and control of the complex chaotic financial system with fractional derivatives

Abstract

We represent a nonlinear time-fractional model of the complex chaotic financial system to understand the occurrences of the interest rate, investment demand and price index in this research. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo with fractional derivative. The stabilization of equilibrium is obtained by both theoretical analysis and the simulation result. A certain threshold value of the basic reproduction number with sensitivity analysis has been made. Stability analysis of the model is confirmed by the Lyapunov equation and detail the stability analysis of this strategy together with the uniqueness of the special solutions. The idea of observability and controllability for linearized control is utilized for feedback control. By utilizing the Laplace Adomian Decomposition technique, the solution of the time-fractional model has been obtained. At last, numerical simulations are given for three fractional-order chaotic systems to check the effectiveness as indicated by the fractional parameter.