Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Anomalous Diffusion (joint session DY/BP)

DY 22.3: Vortrag

Dienstag, 8. März 2016, 14:30–14:45, H47

Scales of Function Spaces for Weyl Fractional Calculus — •Tillmann Kleiner and Rudolf Hilfer — Institute for Computational Physics, University of Stuttgart, Germany

Anomalous diffusion models are frequently based on fractional differential equations [1]. Analytical investigations of these mathematical models require suitable function spaces on which the fractional derivatives operate as continuous operators. This contribution introduces function spaces suitable for Weyl fractional calculus. Scales of locally convex spaces with topology generating seminorms are constructed using weighted maximal functions. These scales are sets of spaces partially ordered by inclusion. Minimal and maximal spaces with respect to this ordering are determined such that Weyl fractional derivatives operate on them continuously or isomorphically. Such spaces can also be determined for sets of linear combinations of these operators with orders restricted to some fixed subset of C. Inclusions of spaces within the scale correspond to continuous injections with dense range. As a result the investigated operators and their inverses are continuous extensions from the subspace of test functions for all suitable spaces.
Applications of Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore, 2000).