Locally one dimensional scheme of the dirichlet boundary value problem for fractional diffusion equation with space caputo fractional derivative

		ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online)

Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Contacts Address: Markusa st. 22, Vladikavkaz, 362027, RNO-A, Russia Phone: (8672)50-18-06 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.7384 Locally one dimensional scheme of the dirichlet boundary value problem for fractional diffusion equation with space caputo fractional derivative Bazzaev A. K. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2. Abstract: 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. Keywords: Caputo fractional derivative, stability and convergence of difference schemes, slow diffusion equation, locally one-dimensional difference scheme. Language: Russian Download the full text For citation: Bazzaev A. K. Locally one dimensional scheme of the dirichlet boundary value problem for fractional diffusion equation with space caputo fractional derivative // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 1, pp.3-13. DOI 10.23671/VNC.2016.2.7384 + References 1. Tarasov V. E. Modeli Teoreticheskoj Fiziki s Integro-Differencirovaniem Drobnogo Porjadka, Moskva, Izhevsk, Izhevskij Institut Komp'juternyh Issledovanij, 2011, 568 p. (Russian). 2. Nahushev A. M. Uravnenija Matematicheskoj Biologii, Moskva, Vysshaja Shkola, 1995, 301 p. (Russian). 3. Chukbar K. V. Stochastic transport and fractional derivatives. Journal of Experimental and Theoretical Physics,1995, vol. 81, no 5, pp. 1025-1029. 4. Olemskij A. N., Flat A. Ja. Ispol'zovanie koncepcii fraktala v fizike kondensirovannoj sredy. Uspehi Fiz. Nauk, 1993, vol. 163, no. 12, pp. 1-50 (Russian). 5. Kobelev V. L., Kobelev Ja. L., Romanov E. P. Nedebaevskaja relaksacija diffuzija vo fraktal'nom prostranstve. Dokl. RAN, 1998, vol. 361, no. 6, pp. 755-758 (Russian). 6. Nigmatullin R. R. Fractional integral and its physical interpretation. Theoretical and Mathematical Physics, 1992, vol. 90, no. 3, pp. 242-251. 7. Lafisheva M. M., Shkhanukov-Lafishev M. Kh. Locally one-dimensional difference schemes for the fractional order diffusion equation. Computational Mathematics and Mathematical Physics, 2008, vol. 48, no. 10, pp. 1875-1884. 8. Bazzaev A. K., Shkhanukov-Lafishev M. Kh. Locally one-dimensional scheme for fractional diffusion equations with robin boundary conditions. Computational Mathematics and Mathematical Physics, 2010, vol. 50, no. 7, pp. 1141-1149. 9. Bazzaev A. K. The third boundary problem for general parabolic differential equation of fractional order in multidimensional field. Vestnik VGU. Ser. Fizika. Matematika [Proc. Voronezh State Univ. Ser. Phys. Math.], 2010, no. 2, pp. 5-14 (Russian). 10. Samarskij A. A. Teorija Raznostnyh Shem. 3-e izd., ispr., Moskva, Nauka, 1989, 616 p. (Russian). 11. Taukenova F. I., Shkhanukov-Lafishev M. Kh. Difference methods for solving boundary value problems for fractional differential equations. Computational Mathematics and Mathematical Physics, 2006, vol. 46, no. 10, pp. 1785-1795. 12. Samarskij A. A., Gulin A. V. Ustojchivost' Raznostnyh Shem, Moskva, Nauka, 1973, 415 p. ← Contents of issue


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