Anomalous diffusion with transient subordinators: a link to compound relaxation laws.

This paper deals with a problem of transient anomalous diffusion which is currently found to emerge from a wide range of complex processes. The nonscaling behavior of such phenomena reflects changes in time-scaling exponents of the mean-squared displacement through time domain - a more general picture of the anomalous diffusion observed in nature. Our study is based on the identification of some transient subordinators responsible for transient anomalous diffusion. We derive the corresponding fractional diffusion equation and provide links to the corresponding compound relaxation laws supported by this case generalizing many empirical dependencies well-known in relaxation investigations.