相关论文: Subdiffusion equation with Cattaneo effect

In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the…

We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…

Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…

A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox…

We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…

Anomalous subdiffusion characterizes transport in diverse physical systems and is especially prevalent inside biological cells. In cell biology, the prevailing model for chemical activation rates has recently changed from the first passage…

The subdiffusion equation with a Caputo fractional derivative of order $\alpha\in(0,1)$ in time arises in a wide variety of practical applications, and it is often adopted to model anomalous subdiffusion processes in heterogeneous media.…

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.…

We investigate the Cauchy problem for a semilinear spatio--temporal fractional diffusion equation with a time-dependent forcing term: \[ \partial_t^\alpha u + (-\Delta)^{\mathsf{s}} u = |u|^p + t^{\sigma}\,\mathbf{w}(x), \quad (t,x) \in…

We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…

In this work, we analyze a Crank-Nicolson type time stepping scheme for the subdiffusion equation, which involves a Caputo fractional derivative of order $\alpha\in (0,1)$ in time. It hybridizes the backward Euler convolution quadrature…

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…

Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…

This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…

An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of…

In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify…

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…

The three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time averaged mean square…

The various types of generalized Cattaneo, called also telegrapher's equation, are studied. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, \textit{i.e.} are…