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By Günter Radons, Rainer Klages, Igor M. Sokolov

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2: Neoclassical Transport (North-Holland, Amsterdam, 1988). 11 12 References 6 F. Mainardi, Yu. Luchko, and G. Pagnini, “The fundamental solution of the spacetime fractional diffusion equation”, Fract. Calc. Appl. Anal. 4, 153 (2001). org/abs/cond-mat/0702419] 7 R. Balescu, “V-Langevin equations, continuous time random walks and fractional diffusion”, Chaos, Solitons and Fractals 34, 62 (2007). 8 P. Allegrini, P. J. West, “Preface”, Chaos, Solitons & Fractals 34, 1 (2007). 9 R. plasma-ph], 19 April 2007, p.

A 38, 344 (1988). 5 R. Balescu, Transport Processes in Plasma: Vol. 1: Classical Transport. Vol. 2: Neoclassical Transport (North-Holland, Amsterdam, 1988). 11 12 References 6 F. Mainardi, Yu. Luchko, and G. Pagnini, “The fundamental solution of the spacetime fractional diffusion equation”, Fract. Calc. Appl. Anal. 4, 153 (2001). org/abs/cond-mat/0702419] 7 R. Balescu, “V-Langevin equations, continuous time random walks and fractional diffusion”, Chaos, Solitons and Fractals 34, 62 (2007). 8 P.

2 Mathematical Introduction to Fractional Derivatives of right- and left-sided Weyl fractional integrals. The conjugate Riesz potential is defined by (Iα f )( x ) = (Iα+ f )( x ) − (Iα− f )( x ) 2 sin(απ/2) 1 = 2Γ(α) sin(απ/2) ∞ −∞ sgn( x − y) f (y) dy. 43). 44) for α = 0. 47) for α = 2k, k ∈ Z. 48) with parameter β ∈ R. The corresponding generalized Riesz–Feller fractional integral of order α and type β is defined as (Iα,β f )( x ) = (K α,β ∗ f )( x ). 49) This formula interpolates continuously from the Weyl integral Iα− = Iα,−π/2 for β = −π/2 through the Riesz integral Iα = Iα,0 for β = 0 to the Weyl integral Iα+ = Iα,π/2 for β = π/2.

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