Abstract

An overview is given on anomalous diffusion processes with emphasis on subdiffusion, which is widespread in many complex systems of different scales. We consider in particular the case of subdiffusion which corresponds to a continuous-time random walk process in which the waiting time for a step is given by a probability distribution with a diverging mean value. Relationships to the fractional diffusion or Fokker-Planck equations and their generalizations will be discussed. Special attention will be given to the problem of the initial conditions and the corresponding aging processes. We will highlight recent results on superdiffusion related to search strategies.