An efficient numerical approach to solve the space fractional FitzHugh–Nagumo model

In this work, we study the numerical approximation for the space fractional FitzHugh–Nagumo model. The numerical scheme is based on the Crank–Nicolson (C–N) method in time and Legendre-spectral method in space. In addition, we prove that the numerical scheme is unconditionally stable. Numerical examples are presented to verify validity of the proposed scheme.