On Dynamical Behaviors and Chaos Control of the Fractional-Order Financial System

In this work, the authors investigate the stability conditions in a fractional-order financial system using the fractional Routh-Hurwitz criteria. According to the qualitative theory, the existence and uniqueness of solutions for a class of commensurate fractional-order financial systems are investigated. A necessary condition for this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than three. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria via linear feedback control method. Then, it is shown that the fractional-order financial system is controllable just in the fractional-order case when using a specific choice of linear controllers. Numerical simulations are used to verify the analytical results.