Related papers: Fractional Hydrodynamic Equations for Fractal Medi…
We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
A generalized Hydrodynamics, referred to as Mesoscopic Hydro-Thermodynamics, of phonons in semiconductors is presented. It involves the descriptions of the motion of the quasi-particle density and of the energy density. The hydrodynamic…
We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $\frac{\partial u}{\partial t} + (-\Delta)^{1/2} (|u|^{m-1}u)=0$ in $\mathbb{R}^N$, with $m>m_*=(N-1)/N$, $N\ge1$ and $f\in…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
In this work, we construct a fractional matter sector for general relativity. In particular, we propose a suitable fractional anisotropy function relating both the tangential and radial pressure of a spherically symmetric fluid based on the…
The equation systems of generalized hydrodynamics, or generalized dynamics for simplicity, for soft-matter quasicrystals were established. Considering the fluidity of the matter with high order we introduced a new elementary…
We derive equations of motion of hydrodynamic fluctuations performing perturbative expansion of the energy-momentum conservation equations around the boost invariant solution in one-dimensional expanding system. In the course of derivation,…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and…
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…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
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…
The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
The problem of wave disturbance propagation in rarefied gas in gravity field is explored. The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous…
A numerical study of fractional Camassa-Holm equations is presented. Smooth solitary waves are constructed numerically. Their stability is studied as well as the long time behavior of solutions for general localised initial data from the…
In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations.…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…