Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Anomalous Transport II (talks contributed by DY)

DY 17.7: Topical Talk

Mittwoch, 24. März 2010, 12:45–13:15, H38

Anomalous Diffusion and Fractional Time — •R. Hilfer — Institut für Computerphysik, Universit"at Stuttgart, 70569 Stuttgart — Institut für Physik, Universit"at Mainz, 55099 Mainz

The intimate relation between anomalous diffusion in the sense of Montroll and fractional diffusion equations has been known for a long time [1]. Its fundamental importance for the theoretical understanding of anomalous diffusion processes is reflected in a growing number of applications to experimental observations [2]. Generalized fractional Riemann-Liouville derivatives of general type appear in these applications. Recently an operational calculus of Mikusiński type was developed for the resulting generalized fractional diffusion equations and their mathematical treatment [3].
[1] R. Hilfer and L. Anton, Phys.Rev.E 51, R848 (1995)
[2] R. Hilfer, in: Anomalous Transport: Foundations and Applications Part I, Chapter 2, pages 17-75, Wiley-VCH, Weinheim (2007)
[3] R. Hilfer, Y. Luchko, Z. Tomovski, Fractional Calculus and Applied Analysis 12, 299 (2009)