in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

The exp((−φ(ξ))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

The exp((-?(?))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Maric...

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation whic...

This paper presents a simple but effective approach for the removal of additive white Gaussian noise from digital images. In our approach, a generalization of a linear heat equation, obtained by replacing time derivative to a fractional time derivative of order between 1 and 2 has been used and a pixel by pixel technique applied. The choice of order of fractional time derivative has been made f...

in this paper, exp-function and (g′/g)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. as a results, some new exact traveling wave solutions are obtained.