Related papers: From Random Times to Fractional Kinetics
Il is argued that the generalisation of the mechanical principles to other variables than localisation, velocity and momentum leads to the laws of generalized dynamics under the condition of continuous and derivable space time. However,…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in…
In this paper we investigate the long-time behavior of the subordination of the constant speed traveling waves by a general class of kernels. We use the Feller--Karamata Tauberian theorem in order to study the long-time behavior of the…
Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$…
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) $L_p$ spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate…
We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we explain the main differences with previous stochastic treatments…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
For non-equilibrium systems of interacting particles and for interacting diffusions in d dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the…