Subordination scenario of anomalous relaxation

The non-exponential relaxation is shown to result from subordination by inverse tempered \alpha-stable processes. The main feature of tempered \alpha-stable processes is a finiteness of their moments, and the class of random processes includes ordinary \alpha-stable processes as a particular case. Starting with the Cole-Cole response this subordination approach establishes its direct link with the Cole-Davidson law. We derive the relaxation function describing the tempered relaxation. The meaning of the empirical response function is clarified.