Function projective synchronization between integer-order and stochastic fractional-order nonlinear systems

•The stochastic processes are combined with the multidimensional fractional-order nonlinear systems.•The function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is considered.•With the stability theory of fractional-order systems and tracking control, a controller is designed.•The method of transforming stochastic error system into an equivalent deterministic system is given.•The proposed method is investigated by integer-order Lorenz system and stochastic fractional-order Chen system.

In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.