Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method

Abstract

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev’s nonequilibrium statistical operator (NSO) method within Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.