Related papers: Fractional statistical dynamics and fractional kin…

Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…

We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…

Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to…

We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…

I discuss the concept of fractional exclusion statistics (FES) and I show that in order to preserve the thermodynamic consistency of the formalism, the exclusion statistics parameters should change if the species of particles in the system…

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional…

This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.

We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…

Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric…

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…

In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…

An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.

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…

Nonlinear fractional dynamics with scale invariance in continuous and discrete time approaches are described. We use non-integer-order integro-differential operators that can be interpreted as generalizations of scaling (dilation)…

We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.

Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…