Related papers: A fast semi-discrete Kansa method to solve the two…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial…
A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue,…
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
In this paper, we propose high-order numerical methods for the Riesz space fractional advection-dispersion equations (RSFADE) on a {f}inite domain. The RSFADE is obtained from the standard advection-dispersion equation by replacing the…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
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…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant…