Lie symmetries, homotopy, non-standard finite difference method for solution of the linear space-fractional telegraph equation

The main purpose of this paper is to use the homotopy analytical method in order to solve the linear space-fractional telegraph differential equation. Also, non-standard finite difference method has been used to solve this equation numerically. Next, the concepts of Lie symmetry is established and the symmetries of the equation are calculated. In this article, Matlab software was used for simulation. Numerical results are presented to evaluate the efficiency and usefulness of the proposed method.