This paper derives physically meaningful boundary conditions for fractional diffusion
equations, using a mass balance approach. Numerical solutions are presented, and …

Bacterial communication is a complex process, which can be formalized by a deterministic
approach and then explored by means of methods of mathematical modeling and computer …

Abstract Space-fractional diffusion problems are investigated from the modeling point of
view. It is pointed out that the elementwise power of the Laplacian operator in R n is an …

In this paper, we focus on the development and study of the finite difference/pseudo-spectral
method to obtain an approximate solution for the time-fractional diffusion-wave equation in a …

In recent decades, variational methods have achieved great success in reducing noise
owing to the use of total variation (TV). The TV-based denoising model introduced by Rudin …

The advection–dispersion phenomenon can be observed in various fields of science.
Mathematically, this process can be studied by considering empirical models, high-order …

Even in the one-dimensional case, dealing with the analysis of space-fractional differential
equations on finite domains is a difficult issue. On a finite interval coupled with zero flux …

In this paper, we obtain some results of the existence and uniqueness of a generalized
solution for a singular fractional initial boundary value problem in the Caputo sense subject …

A finite element numerical method is investigated for fractional order elliptic boundary value
problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an …

This study is devoted to the construction and software implementation of a computational
algorithm for modeling the process of anomalous diffusion. The mathematical model is …