期刊
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
卷 21, 期 6, 页码 955-967出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217979207036771
关键词
Fokker-Planck equation; non-Hamiltonian systems; fractal; fractional integral
The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker-Planck equation is obtained.
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