In this paper, the Mickens non-standard discretization method which effectively preserves the dynamical behavior of linear differential equations is adapted to solve numerically the fractional order hyperbolic partial differential equations. The fractional derivative is described in the Riesz sense. Special attention is given to study the stability analysis and the convergence of the proposed method. Numerical studies for the model problems are presented to confirm the accuracy and the effectiveness of the proposed method. The obtained results are compared with exact solutions and the standard finite difference method.