He's variational iteration method (VIM) is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.

In recent years, there has been a great deal of interest in fractional differential equations since there have been a wide variety of applications in physics and engineering. The space and time fractional telegraph equations have been studied by Orsingher and Zhao [

We note that the space and time fractional derivatives are considered in Caputo sense in this paper. The main objective of the present paper is to extend the application of the variational iteration method (VIM) to obtain approximate solution of the space and time fractional telegraph equations.

We will give a brief description of He's variational iteration method. The basic concepts of the variational iteration method can be expressed as follows. Consider the differential equation of the form

For

Further information about fractional derivatives and its properties can be found in [

In this section we will obtain iteration formulas for space-time fractional telegraph equations. We first consider the following space fractional telegraph equation for

We will give the following three examples to illustrate variational iteration method for solving the space and time fractional telegraph equations.

We first consider the following one-dimensional initial and boundary value problem of space-fractional homogeneous telegraph equation for

The surfaces related with the solution of (

The exact solution

The second-order approximate solution

The surfaces show the second-order approximate solutions of (

We now consider the following one-dimensional initial and boundary value problem of space-fractional inhomogeneous telegraph equation for

The surfaces related with the solution of (

The exact solution

The second-order approximate solution

The surfaces show the second-order approximate solutions of (

We last consider the following initial and boundary value problem of time fractional telegraph equation of order

The variational iteration method has been successfully applied for finding the solution of space and time fractional telegraph equations. The space and time fractional derivatives are considered in the Caputo sense. We have achieved a very good agreement between the approximate solution obtained by He's VIM and the exact solution. The results of the examples show that He's variational iteration method is reliable and efficient method for solving space and time fractional telegraph equations and also other equations.