A numerical solution method for over-damped fractional Langevin equation based on predictive correction approach

Stochastic resonance (SR) is a signal processing method that uses noise to enhance the energy of weak signals. This feature makes it show great potential application value in various fields. Moreover, the memory effect on the past state in time also allows SR to achieve better application and development in the fractional order system. Currently, most of the solutions to fractional SR systems use block diagram simulation methods which are based on the Simulink environment. The simulation solution method solves the system model by putting the fractional calculus into the complex frequency domain, but the complicated calculation and low efficiency make it unable to be conveniently applied to engineering practice. Therefore, this paper proposes a numerical solution method based on predictive correction approach for this problem, and the effectiveness of the proposed method is verified through simulation experiments.