Electron. J. Diff. Equ., Vol. 2014 (2014), No. 97, pp. 1-17.

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

Allaberen Ashyralyev, Nazar Emirov, Zafer Cakir

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.

Submitted December 26, 2013. Published April 10, 2014.
Math Subject Classifications: 35R11, 35B35, 47B39, 47B48.
Key Words: Fractional parabolic equations; Dirichlet-Neumann conditions; positive operator; difference schemes; stability.

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Allaberen Ashyralyev
Department of Mathematics, Fatih University
Buyukcekmece, Istanbul, Turkey
email: aashyr@fatih.edu.tr
Nazar Emirov
Department of Mathematics, Fatih University
Buyukcekmece, Istanbul, Turkey
email: nazaremirov@gmail.com
Zafer Cakir
Department of Mathematical Engineering
Gumushane University, Gumushane, Turkey
email: zafer@gumushane.edu.tr

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