Related papers: Subdiffusion equation with Cattaneo effect
In this paper, we study a time-fractional subdiffusion equation with a nonlinear nonlocal initial condition involving the unknown solution at the final time. The considered problem is formulated using the Caputo fractional derivative of…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
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…
Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms…
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…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation of order $\alpha$ and supply it with the fast and oblivious implementation. In particular, we find a condition for the CQ to be admissible and…
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 $d$,…
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…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
A class of discrete time random walks has recently been introduced to provide a stochastic process based numerical scheme for solving fractional order partial differential equations, including the fractional subdiffusion equation. Here we…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…