Subordination scenario of anomalous relaxation

Abstract

The non-exponential relaxation is shown to result from subordination by inverse tempered α-stable processes. The main feature of tempered α-stable processes is a finiteness of their moments, and the class of random processes includes ordinary α-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.

14 pages, 3 figures

References in corpus (3)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Fractional dynamics from the ordinary Langevin equation
• The Stochastic Nature of Complexity Evolution in the Fractional Systems

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