We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.

Abstract. In this paper, we first consider the numerical method that Lin and Xu proposed and analyzed in [Finite difference/spectral approximations for the time-fractional diffusion equation, JCP 2007] for the time-fractional diffusion equation. It is a method basing on the combination of a finite different scheme in time and spectral method in space. The numerical analysis carried out in that ...

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding exact solutions of (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown transform given into (1+1)-dimensional procedure. Also, explain derive reduced equations method. Additionally, this careful and systematic study, will investigate find ...

In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on th...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

In this paper, a technique generally known as meshless method is presented for solving fractional partial differential equations (FPDEs). Some physical linear and nonlinear experiments such as time-fractional convective-diffusion equation, timefractional wave equation and nonlinear space-fractional Fisher's equation are considered. We present the advantages of using the radial basis functions (...

The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are s...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...