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

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 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. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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