Related papers: Fractional Immigration-Death Processes
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
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…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders,…
In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
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…
Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from…