Locally one dimensional scheme of the Dirichlet boundary value problem for fractional diffusion equation with space Caputo fractional derivative
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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Locally one-dimensional difference schemes for the fractional diffusion equation with space Caputo fractional derivative in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.
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A. K. Bazzaev. Locally one dimensional scheme of the Dirichlet boundary value problem for fractional diffusion equation with space Caputo fractional derivative. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a0/

[1] Tarasov V. E., Modeli teoreticheskoi fiziki s integro-differentsirovaniem drobnogo poryadka, Izhevskii institut kompyuternykh issledovanii, M.–Izhevsk, 2011, 568 pp.

[2] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 301 pp.

[3] Chukbar K. V., “Stokhasticheskii perenos i drobnye proizvodnye”, ZhETF, 108:5(11) (1995), 1875–1884

[4] Olemskii A. N., Flat A. Ya., “Ispolzovanie kontseptsii fraktala v fizike kondensirovannoi sredy”, Uspekhi fiz. nauk, 163:12 (1993), 1–50 | DOI

[5] Kobelev V. L., Kobelev Ya. L., Romanov E. P., “Nedebaevskaya relaksatsiya diffuziya vo fraktalnom prostranstve”, Dokl. RAN, 361:6 (1998), 755–758 | MR | Zbl

[6] Nigmatullin R. R., “Drobnyi integral i ego fizicheskaya interpretatsiya”, Teoreticheskaya i matem. fizika, 90:3 (1992), 354–368 | MR | Zbl

[7] Lafisheva M. M., Shkhanukov-Lafishev M. Kh., “Lokalno-odnomernaya skhema dlya uravneniya diffuzii drobnogo poryadka”, ZhVM i MF, 48:10 (2008), 1878–1887 | MR | Zbl

[8] Bazzaev A. K., Shkhanukov M. Kh., “Lokalno-odnomernaya skhema dlya uravneniya diffuzii drobnogo poryadka s kraevymi usloviyami III roda”, ZhVM i MF, 50:7 (2010), 1200–1208 | MR | Zbl

[9] Bazzaev A. K., “Tretya kraevaya zadacha dlya obobschennogo uravneniya parabolicheskogo tipa c drobnoi proizvodnoi po vremeni v mnogomernoi oblasti”, Vestn. VGU. Ser. Fizika. Matematika, 2010, no. 2, 5–14

[10] Samarskii A. A., Teoriya raznostnykh skhem, 3-e izd., ispr., Nauka, M., 1989, 616 pp. | MR

[11] Taukenova F. I., Shkhanukov-Lafishev M. Kh., “Raznostnye metody resheniya kraevykh zadach dlya differentsialnykh uravnenii drobnogo poryadka”, ZhVM i MF, 46:10 (2006), 1871–1881 | MR

[12] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Nauka, M., 1973, 415 pp.