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Consequently, his interesting contribution for the Denton special issue appeared posthumous [7]: the Guest Editors dedicated that issue to his memory, see [8]. The abstract of his invited lecture at Bad Honnef has been included by the Editors in the present book. The last version of his lecture notes on anomalous transport, based on the applications of fractional calculus (the object of our exchange of e-mails), was submitted by his colleagues to the Physics section of the Cornell University Archives in April 2007, see [9].

39) for α > 0. 40) is the Heaviside unit step function, and x α = exp α log x with the convention that log x is real for x > 0. 2) in Appendix C. Note that K± loc for α > 0. 4 Riesz Fractional Integrals Riemann–Liouville and Weyl fractional integrals have upper or lower limits of integration, and are sometimes called left-sided resp. right-sided integrals. A more symmetric definition was advanced in [97]. 3 Let f ∈ L1loc (R ) be locally integrable. The Riesz fractional integral or Riesz potential of order α > 0 is defined as the linear combination [99] (Iα f )( x ) = (Iα+ f )( x ) + (Iα− f )( x ) 2 cos(απ/2) 1 = 2Γ(α) cos(απ/2) ∞ −∞ f (y) dy | x − y |1− α 4) If K, f ∈ L1 (R ) then ( K ∗ f )( t) exists for almost all t ∈ R and f ∈ L1 (R ).

39) for α > 0. 40) is the Heaviside unit step function, and x α = exp α log x with the convention that log x is real for x > 0. 2) in Appendix C. Note that K± loc for α > 0. 4 Riesz Fractional Integrals Riemann–Liouville and Weyl fractional integrals have upper or lower limits of integration, and are sometimes called left-sided resp. right-sided integrals. A more symmetric definition was advanced in [97]. 3 Let f ∈ L1loc (R ) be locally integrable. The Riesz fractional integral or Riesz potential of order α > 0 is defined as the linear combination [99] (Iα f )( x ) = (Iα+ f )( x ) + (Iα− f )( x ) 2 cos(απ/2) 1 = 2Γ(α) cos(απ/2) ∞ −∞ f (y) dy | x − y |1− α 4) If K, f ∈ L1 (R ) then ( K ∗ f )( t) exists for almost all t ∈ R and f ∈ L1 (R ).

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