Stochastic foundations of fractional dynamics

Abstract

It is shown that fractional diffusion equations arise very naturally as the limiting dynamic equations of all continuous time random walks with decoupled temporal and spatial memories and with either temporal or spatial scale invariance (fractal walks), thus enlarging their stochastic foundations hitherto restricted to a particular case of fractal walk [R. Hilfer and L. Anton, Phys. Rev. E 51, R848 (1995)].