3 research outputs found
Transport Equations from Liouville Equations for Fractional Systems
We consider dynamical systems that are described by fractional power of
coordinates and momenta. The fractional powers can be considered as a
convenient way to describe systems in the fractional dimension space. For the
usual space the fractional systems are non-Hamiltonian. Generalized transport
equation is derived from Liouville and Bogoliubov equations for fractional
systems. Fractional generalization of average values and reduced distribution
functions are defined. Hydrodynamic equations for fractional systems are
derived from the generalized transport equation.Comment: 11 pages, LaTe
Fractional Systems and Fractional Bogoliubov Hierarchy Equations
We consider the fractional generalizations of the phase volume, volume
element and Poisson brackets. These generalizations lead us to the fractional
analog of the phase space. We consider systems on this fractional phase space
and fractional analogs of the Hamilton equations. The fractional generalization
of the average value is suggested. The fractional analogs of the Bogoliubov
hierarchy equations are derived from the fractional Liouville equation. We
define the fractional reduced distribution functions. The fractional analog of
the Vlasov equation and the Debye radius are considered.Comment: 12 page
Fractional Liouville and BBGKI Equations
We consider the fractional generalizations of Liouville equation. The
normalization condition, phase volume, and average values are generalized for
fractional case.The interpretation of fractional analog of phase space as a
space with fractal dimension and as a space with fractional measure are
discussed. The fractional analogs of the Hamiltonian systems are considered as
a special class of non-Hamiltonian systems. The fractional generalization of
the reduced distribution functions are suggested. The fractional analogs of the
BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page