with the Riesz space-fractional derivative of order 0 < α ≤ 2 in the presence of the linear potential V(x) = βx. The wave function to the one-dimensional Schrödinger equation in momentum space is given in closed form allowing the determination of other measurable quantities such as the mean square displacement. Analytical solutions are derived for the relevant case of α = 1, which are useable f...

A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on nonuniform meshes. It is based on the utilization of hierarchical matrices (H-Matrices) for the representation of the stiffness matrix resulting from the finite element discretization of the FDEs. We employ a geometric multigr...

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/jn mj. Continuous medium equation for this system can be obtained in the socalled infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of mot...

In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in sense of Riesz derivative, we explore coupled Hirota equation give its explicit form. Unlike previous equations, type is integrable. Therefore, obtain $n$-soliton solutions inverse scattering transformation reflectionless case. particular, analyze one- two-soliton prove that can also be regarded a...

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, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Fractional nonlinear reaction-diffusion models have found numerous applications in patten formation in biology, chemistry, physics and Engineering. Obtaining analytical solutions of fractional nonlinear reaction-diffusion models is difficult, generally numerica...