A non-Markov kinetic equation with fractional derivatives for a nonequilibrium one-particle distribution function is obtained. The resulting equation contains the generalized diffusion and friction coefficients in the space of coordinates and momentums of particles. This equation can be used, in particular, for mathematical modeling of kinetic processes of particle transport in porous media with fractal structure.
The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo--Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations for the Cattaneo--Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.
The new non-Markovian electrodiffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-type diffusion equation with taking into account fractality of space-time are obtained. Different models of the frequency dependence of memory functions, which lead to known diffusion equations with fractality of space-time and their generalizations are considered.