Anomalous Transport Foundations and Applications by Günter Radons, Rainer Klages, Igor M. Sokolov
By Günter Radons, Rainer Klages, Igor M. Sokolov
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Additional resources for Anomalous Transport Foundations and Applications
A brief introduction to distributions is given in Appendix C. 37) to distributions one must deﬁne the convolution of two distributions. To do so one multiplies Eq. 38) on both sides with a smooth test function ϕ ∈ Cc∞ (R ) of compact support. 52) where the notation f (y), ϕ( x + y) means that the functional F f is applied to the function ϕ( x + ·) for ﬁxed x. 2 Mathematical Introduction to Fractional Derivatives where ϕ x (·) = ϕ( x + ·). 52) can be used as a deﬁnition for the convolution of distributions provided that the right-hand side has meaning.
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E. E. Ph. van Milligen, “Renormalization of tracer turbulence leading to fractional differential equations”, Phys. Rev. E 74, 016305 (2006). 2 R. A. Carreras, and B. Ph. van Millegen, “Radu Balescu and the search for a stochastic description of turbulent transport in plasma”, Phys. Ann. Univ. Cracovia 17, 27 (2007) (special issue In Memoriam of Radu C. Balescu (1932–2006)). 3 M. De Leener, J. Orban, M. Pettini, A. H. Misguich, and R. Balescu, in Proceedings of the Congrès Société Francaise de Physique, Nice, 1985, Bull.