M ar 2 00 7 Langevin Approach to Fractional Diffusion Equations including Inertial Effects
نویسندگان
چکیده
In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H., we show how these equations are related to Langevin equations via the procedure of subor-dination. Introduction. – Some 70 years ago, Kramers [1] considered the motion of a Brownian particle subject to a space-dependent force F(x) per unit mass. His goal was to compute the joint probability distribution f (x, u, t) for finding a particle at time t at the position x with the velocity u. For this quantity he could derive the famous Kramers-Fokker-Planck (KFP) equation [2, 3]
منابع مشابه
Langevin approach to fractional diffusion equations including inertial effects.
In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby (Fogedby, H. C. Phys. Rev. E 1994, 50, 041103), we show how these equations are related to Langevin equations via the procedure of subordination.
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