A ghost structure finite difference method for a fractional FitzHugh-Nagumo monodomain model on moving irregular domain

•The ghost structure (GS) method can simulate the fractional monodomain model on a moving irregular domain.•The GS method can deal effectively with the approximating domain-dependent fractional derivatives.•Two fast algorithms are proposed to compute the time-consuming integral transformation between different variables.•Results show the changes of spatial derivatives can affect the propagation of potential wave.