Geodesic
On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 183-187

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Difference approximation for the Caputo fractional derivative of the $4-\beta$, $1\beta\leq 2$, order is obtained in the work. The difference schemes for solving the Dirichlet problem for the Poisson equation with fractional derivatives are developed. The right part and initial data stability of difference problem and its convergence are proved.
Mots-clés : Poisson's equation
Keywords: Dirichlet problem, fractional order derivative, numerical method, approximation, difference problem. 
@article{VSGTU_2012_2_a21,
     author = {V. D. Beybalaev},
     title = {On the numerical solution of the {Dirihlets} problem for the {Poisson's} equation with fractional order derivatives},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {183--187},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/}
}
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V. D. Beybalaev. On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 183-187. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/