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Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional wave equation (FWE) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Legendre approximations. The properties of Legendre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which solved using the finite difference method (FDM). Numerical solutions of FWE are presented and the results are compared with the exact solution. Received: March 7, 2012 c © 2013 Academic Publications, Ltd. url: www.acadpubl.eu §Correspondence author 308 M.M. Khader, N.H. Sweilam, T.A. Assiri

ON THE NUMERICAL SOLUTION FOR THE FRACTIONAL WAVE EQUATION USING LEGENDRE PSEUDOSPECTRAL METHOD