• Natalja O. Gordeeva
  • Ekaterina N. Manaeva
  • Ilona M. Primak
  • Irina I. Palasheva
Keywords: fractional differential equations, heat and mass transfer equation, numerical methods, approximation with fractional derivatives


The paper proposes a numerical solution for the mixed problem concerning a three-dimensional heat transfer fractional differential equation, based on the finite difference method. To solve this problem, an explicit difference scheme described in the paper is used. The stability of a proposed difference scheme is proved. The case of homogeneous medium and a square grid is considered.


Download data is not yet available.


Golovizin V.M., Kisilev V.P., Korotkin I.A. Numerical methods for solving the fractional diffusion equation in the one-dimensional case: Preprint No. IBRAE-2002-10. Moscow: IBRAE RAS, 2002.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo. 2006. Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies). Elsevier Science Inc., New York, NY, USA. ISBN:0444518320.

Bajlekova E. Fractional Evolution Equations in Banach Spaces. Ph. D. Thesis. Eindhoven University of Technology. 2001. – 117 p. url: (Accessed on 30.12.2018)

Glushak A.V., Primak I.M. Boundary value problems for abstract differential equations with fractional derivatives / Scientific Bulletin of the BelSU. Series: Mathematics. Physics. ISSN: 2075-4639, 2011. - â„–17 (112). - Issue 24. - Pp.125-140.

Primak I.M. Boundary value problems for abstract fractional differential equations with a bounded operator./Scientific Bulletin of the BelSU. Series: Mathematics. Physics. ISSN: 2075-4639, 2013. - â„–5 (148). - Issue 30. - Pp.98-106.

Nakhushev A.M. Fractional calculus and its application. Moscow: Fizmatlit, 2003. 272 p.

Beibalaev V.D., Shabanova M.R. A numerical method for solving a boundary value problem for a two-dimensional heat transfer equation with fractional derivatives. Herald of the Samara State Technical University. Series: Physics and mathematics. - 2010. - № 5 (21). - pp. 244–251.

Accessed from: (Accessed on 14.01.2019)

Taukenova F. I., Shkhanukov-Laï¬shev M.Kh. Difference methods for solving boundary value problems for fractional-order differential equations // Comput. Math. Math. Phys., 2006. — Vol. 46, No. 10. — P. 1785–1795. url: (accessed on 22.02.2019)

Lynch V.E., Carreras B.A., del-Castill-Negrete D., Ferreira-Mejias K.M., Hicks H.R. Numerical methods for the solution of partial differential equations of fractional order // J. Comput. Phys., 2003. — Vol. 192, No. 2. — Pp. 406–421

Babenko Yu.I. The fractional differentiation method in applied problems of heat and mass transfer theory. - SPb: NPO Professional, 2009, 584 p.

S. B. Yuste, and L. Acedo. “An Explicit Finite Difference Method and a New Von Neumann-Type Stability Analysis for Fractional Diffusion Equations.†SIAM Journal on Numerical Analysis, vol. 42, no. 5, 2005, pp. 1862–1874. JSTOR,

Samko S.G., Kilbas A.A., Marichev O.I. Fractional integrals and derivatives and some of their applications. Minsk: Science and technology, 1987, 688 p.

Samko S.G., Kilbas, A.A. and O.I. Marichev: Fractional Integrals and Derivatives,: Theory and Applications, Gordon and Breach, Amsterdam 1993. [Engl. Transi, from Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk 1987]â€

Daletsky Yu.L., Krein M.G. Stability of solutions of differential equations in a Banach space. Nauka, Moscow, 1970. - 536 p.

How to Cite
Gordeeva, N. O., Manaeva, E. N., Primak, I. M., & Palasheva, I. I. (2019). USE OF FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF THREE-DIMENSIONAL HEAT TRANSFER FRACTIONAL DIFFERENTIAL EQUATION. COMPUSOFT: An International Journal of Advanced Computer Technology, 8(6). Retrieved from