Anomalous diffusion and relaxation in macromolecular systems

Scaling, namely the algebraic (power-law) dependence of measured properties on frequency or time is of wide-spread occurrence in polymeric systems. In this work we highlight its connection to fractional calculus. As examples of systems that obey scaling, we discuss here linear and fractal generalized Gaussian structures. On the other hand, non-scaling behavior is also found in many realistic situations. In the second part of the paper we consider as example of non-scaling behavior the relaxation of small-world networks. Detailed measurements, such as provided by dielectric spectroscopy or mechanical relaxation can help to determine the basic, mesoscopic properties of the substances under investigation.