in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

in this paper, a new numerical method for solving time-fractional diffusion equations is introduced. for this purpose, finite difference scheme for discretization in time and chebyshev collocation method is applied. also, to simplify application of the method, the matrix form of the suggested method is obtained. illustrative examples show that the proposed method is very efficient and accurate.

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

This work investigates how we can extend the invariant subspace method to $$(2+1)$$ -dimensional time-fractional non-linear PDEs. More precisely, systematic study has been provided for constructing various dimensions of subspaces generalized convection–reaction–diffusion wave equation along with initial conditions first time. Additionally, special types above-mentioned are discussed through thi...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

In recent years, fractional differential equations are widely used in the many academic disciplines--viscoelastic mechanics, Fractal theory and so on. Furthermore, fractional differential equations can be used to describe some abnormal phenomenon. For instance, fractional convection-diffusion equation can be used to describe the fluid of abnormal infiltration phenomenon in the medium. In this p...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...