This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, m...

variational iteration method using he's polynomials can be used to construct solitary solution and  compacton-like solution for nonlinear dispersive equatioons. the chosen initial solution can be determined in compacton-like form or in solitary form with some compacton-like or solitary forms with some unknown parameters, which can be determined in the solution procedure. the compacton-like solu...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by variational iteration method (VIM). By using initial conditions, the expli...

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

Variational iteration method has been favourably applied to various kinds of nonlinear problems. The main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper recent trends and developments in the use of the method are reviewed. Major applications to nonlinear wave equation, nonlinear fractional differential equations, ...