Synchronization for fractional FitzHugh–Nagumo equations with fractional Brownian motion

This paper is devoted to dynamics of the Caputo‐type fractional FitzHugh–Nagumo equations (FHN) driven by fractional Brownian motion (fBm). The existence and uniqueness of mild solution for of the Caputo‐type fractional FHN are established, and the exponential synchronization and finite‐time synchronization for the stochastic FHN are provided. Finally, the numerical simulation of the synchronization for time‐fractional FHN perturbed by fBm is provided; the effects of the order of time fractional derivative and Hurst parameter on synchronization are also revealed.