Abstract: In this paper, the synchronization problem of hyperchaotic fractional-order financial systems with uncertainty and outer disturbances are studied based on the sliding mode control and integral sliding mode control techniques. Two sufficient conditions are established to ensure the fractional-order uncertain hyperchaotic financial systems acquiring sliding mode and integral sliding mode synchronization by designing sliding mode functions and controllers through founding adaptive rules using fractional-order integral and calculus. The conclusions are verified by Matlab numerical simulations. The sliding mode functions, controllers and adaptive rules which are designed in the paper can be planted for studying sliding mode synchronization of integer-order chaotic systems. The approaches used in the paper supply the techniques to study the fractional-order systems and can be extended to the integer-order systems synchronization problems.

Key words: uncertain, hyperchaotic, integral sliding mode, outer disturbance