Abstract
This paper introduces a fractional-order financial risk system for the first time. Employing well-known tools and analyses such as bifurcations diagrams and spectral entropy, the dynamical behaviors of the system associated with fractional derivative are investigated. The impacts of the fractional derivative on the system's behavior and its dynamical feature are shown. Then, tracking control and stabilization of the systems are studied. As it is obvious, the existence of faults and failures in the process of control of financial and economic systems is undeniable - this issue necessitates applying proper control techniques for the systems. So as to achieve appropriate results in the control of fractional financial risk system, two finite-time fault-tolerant controllers are proposed, namely, finite-time active fault-tolerant control and finite-time passive fault-tolerant control. Not only do these techniques force the system to reach desired values in finite time, but also, the proposed techniques are robust against uncertainties, faults, and failures in actuators. Through finite-time observers, the effects of all uncertainties are taken to account in the active controller. Finally, numerical simulations of tracking control and stabilization are presented. For numerical simulations, the fractional financial risk system is considered to be in the presence of unknown disturbance as well as faults and failures in actuators. It is assumed that the system is in the presence of various types of actuator faults. Numerical results affirm the ability of the offered control techniques for pushing the states of the fractional-order risk system to the desired value in a short period of time.