Copyright © 2012 Allaberen Ashyralyev and Zafer Cakir. 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 first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive
stability estimates for the solution of these difference schemes are obtained. A procedure of modified
Gauss elimination method is used for solving these difference schemes in the case of one-dimensional
fractional parabolic partial differential equations.