Control and switching synchronization of chaotic finance systems with integer and non-integer orders

This paper discusses the effect of the integer and non-integer orders of the finance chaotic systems where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, we develop a framework to obtain approximate numerical solutions of the integer and non-integer orders finance chaotic system using a non-standard finite difference and Adam Bashforth Moulton predictor corrector methods. The concept of synchronization of different fractional order chaotic systems using active control technique is presented. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability.