Geodesic
The difference methods for solution of the Dirichlet boundary value problem for the fractional
News of the Kabardin-Balkar scientific center of RAS, no. 6 (2016), pp. 45-50.

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Moisture movement in capillary porous media is described by Aller's equation of [1]. Solution of boundary value problem for the fractional Aller's equation in differential and difference settings is studied. By the method of energy inequalities for the solution of the difference problem we obtain a priori estimates.
Keywords: fractional derivative, a priori estimate, difference scheme, stability and convergence. 
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Ph. A. Karova. The difference methods for solution of the Dirichlet boundary value problem for the fractional. News of the Kabardin-Balkar scientific center of RAS, no. 6 (2016), pp. 45-50. http://geodesic.mathdoc.fr/item/IZKAB_2016_6_a6/

[1] A. F. Chudnovskii, Teplofizika pochv, Nauka, M., 1976, 137 pp.

[2] A. A. Alikhanov, “Boundary value problems for the diffusion equation of the variable order in differential and difference settings”, Appl. Math. Comput, 2012, no. 219, 3938–3946 | MR | Zbl

[3] A. A. Alikhanov, “Apriornye otsenki reshenii kraevykh zadach dlya uravnenii drobnogo poryadka”, Differents. uravneniya, 46:5 (2010), 658–664 | MR | Zbl

[4] A. A. Alikhanov, “A new difference scheme for the time fractional diffusion equation”, J. Comput. Phys, 2015, no. 280, 424–438 | DOI | MR | Zbl