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• W2022679153 abstract "Abstract This paper presents extensions to the classical stochastic Liouville equation of motion that contain the Riemann-Liouville and Caputo time-fractional derivatives. At first, the dynamic equations with the time-fractional derivatives are formally obtained from the classical Liouville equation. A feature of these new equations is that they have the same common formal solution as the classical Liouville equation and therefore may be used for study of the Hamiltonian system dynamics. Two cases of the time-dependent and time-independent Hamiltonian are considered separately. Then, the time-fractional Liouville equations are deduced from the short- and long-time asymptotic expansions of the obtained dynamic equations. The physical meaning of the resulting equations is discussed. The statements of the Cauchy-type problems for the derived time-fractional Liouville equations are given, and the formal solutions of these problems are presented. At last, the projection operator formalism is employed to derive the time-fractional extensions of the Zwanzig kinetic equations and the corresponding formal statistical operators from the time-fractional Liouville equations." @default.
• W2022679153 created "2016-06-24" @default.
• W2022679153 creator A5046956687 @default.
• W2022679153 date "2013-01-01" @default.
• W2022679153 modified "2023-10-16" @default.
• W2022679153 title "Time-fractional extensions of the Liouville and Zwanzig equations" @default.
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• W2022679153 doi "https://doi.org/10.2478/s11534-013-0229-x" @default.
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