Related papers: Solutions For A Generalized Fractional Anomalous D…
Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when…
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $\beta \in (0,1)$. The fundamental solution for the Cauchy problem is…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
The optimization of the usual entropy $S_1[p]=-\int du p(u) ln p(u)$ under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
The generalised Boltzmann equation which treats the combined localised and delocalised nature of transport present in certain materials is extended to accommodate time-dependent fields. In particular, AC fields are shown to be a means to…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$,…
Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…