Copyright © 2012 Allaberen Ashyralyev and Fadime Dal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The numerical and analytic solutions of the mixed
problem for multidimensional fractional hyperbolic partial
differential equations with the Neumann condition are presented. The
stable difference scheme for the numerical solution of the mixed
problem for the multidimensional fractional hyperbolic equation with
the Neumann condition is presented. Stability estimates for the
solution of this difference scheme and for the first- and second-order difference derivatives are obtained. A procedure of modified
Gauss elimination method is used for solving this difference scheme
in the case of one-dimensional fractional hyperbolic partial
differential equations. He's variational iteration method is
applied. The comparison of these methods is presented.