Ashyralyev, Allaberen; Emirov, Nazar; Cakir, Zafer

We study initial-boundary value problems for fractional parabolic equations with the Dirichlet-Neumann conditions. We obtain a stable difference schemes for this problem, and obtain theorems on coercive stability estimates for the solution of the first order of accuracy difference scheme. A procedure of modified Gauss elimination method is applied for the solution of the first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.

Ashyralyev, Allaberen; Emirov, Nazar; Cakir, Zafer; Ashyralyev, A; Lukashov, A

The multidimensional fractional parabolic equation with the Dirichlet-Neumann condition is studied. Stability estimates for the solution of the initial-boundary value problem for this fractional parabolic equation are established. The stable difference schemes for this problem are presented. Stability estimates for the solution of the first order of accuracy difference scheme are obtained. A procedure of modified Gauss elimination method is applied for the solution of first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.