Numerical Methods of Solution of the Dirichlet Boundary Value Problem for the Fractional Allers’ Equation

  • Fatimat A. KarovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)


Solution of Dirichlet boundary value problem for the Allers’ equation in differential and difference settings are studied. By the method energy inequalities, a priori estimate is obtained for the solution of the differential problems.


Difference Scheme Dirichlet Boundary Fractional Derivative Fractional Calculus Viscoelastic Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Chudnovsky, A.F.: Thermophysics Soil. Nauka, Moscow (1976). p. 137. (in Russian)Google Scholar
  2. 2.
    Shkhanukov-Lafishev, M.Kh.: About boundary value problems for equation of the third order. Differ. Equ. 18(4), 1785–1795 (1982)Google Scholar
  3. 3.
    Alikhanov, A.A.: Boundary value problems for the diffusion equation of the variable order in differential and difference settings. Appl. Math. Comput. 219, 3938–3946 (2012)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Alikhanov, A.A.: A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280, 424–438 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Wu, Ch.: Numerical solution for Stokes’ first problem for a heated generalized second grade fluid with fractional derivative. Appl. Num. Math. 59, 2571–2583 (2009)Google Scholar
  6. 6.
    Shkhanukov-Lafishev, M.Kh., Taukenova, F.I.: Difference methods for solving boundary value problems for fractional differential equations. Comput. Math. Math. Phys. 46(10), 1785–1795 (2006)Google Scholar
  7. 7.
    Alikhanov, A.A.: Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation. Appl. Math. Comput. 268, 12–22 (2015)MathSciNetGoogle Scholar
  8. 8.
    Alikhanov, A.A.: A priori estimates for solutions of boundary value problems for fractional-order equations. Differ. Equ. 46(5), 660–666 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and AutomationRussian Academy of SciencesNalchikRussia

Personalised recommendations