Well-posedness of fractional parabolic differential and difference equations with Dirichlet-Neumann conditions

Abstract

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.

Keywords

• Fractional parabolic equations
• Dirichlet-Neumann conditions
• positive operator
• difference schemes
• stability