Abstract
In this work, a novel financial model based on a recent nonsmooth fractional order Caputo-Fabrizio derivative is introduced. The conditions for the existence and uniqueness of the solution of the proposed model are obtained. The local stability analysis of admissible and boundary equilibrium points along with possible local bifurcations are discussed. The key dynamical properties of the model are investigated through obtaining regions of stability, phase portraits and bifurcation diagrams. Chaos synchronization between two master/slave fractional-order financial models is achieved based on the adaptive control theory. In particular, the more realistic case where the values of the master system's parameters are unknown. In addition, the scheme of active chaos synchronization is examined for the suggested system's behavior. Finally, numerical simulations are given to validate the analytical results.
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