Modeling of subdiffusion in space-time-dependent force fields beyond the fractional Fokker-Planck equation

Abstract

In this paper we attack the challenging problem of modeling subdiffusion with an arbitrary space-time-dependent driving. Our method is based on a combination of the Langevin-type dynamics with subordination techniques. For the case of a purely time-dependent force, we recover the death of linear response and field-induced dispersion -- two significant physical properties well-known from the studies based on the fractional Fokker-Planck equation. However, our approach allows us to study subdiffusive dynamics without referring to this equation.