A study of the subdiffusive fractional Fokker–Planck equation of bistable systems

We study the dynamical properties of bistable systems described by the one-dimensional subdiffusive fractional Fokker–Planck equation, for the natural boundary conditions as well as the absorbing boundary conditions. We have investigated the propagators, the auto-correlation function, the survival probability and the lifetime distribution for two model potentials: (1) the quartic double-well potential U4(x)=(−0.5x2+0.25x4), and (2) the sextic double-well potential U6(x)=(−0.75x4+0.5x6). For both potentials, the evolution of the propagator P(x,t|0,0) shows a trimodal transient, in contrast with the result of the conventional Fokker–Planck Theory.