Geodesic
Well-posedness of fractional parabolic differential and difference equations with Dirichlet-Neumann conditions
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35R11, 35B35, 47B39, 47B48
Keywords: fractional parabolic equations, Dirichlet-Neumann conditions, positive operator, difference schemes, stability 
@article{EJDE_2014__2014__a120,
     author = {Ashyralyev,  Allaberen and Emirov,  Nazar and Cakir,  Zafer},
     title = {Well-posedness of fractional parabolic differential and difference equations with {Dirichlet-Neumann} conditions},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1286.35247},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a120/}
}
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Ashyralyev,  Allaberen; Emirov,  Nazar; Cakir,  Zafer. Well-posedness of fractional parabolic differential and difference equations with Dirichlet-Neumann conditions. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a120/