Russian Mathematics

, Volume 63, Issue 2, pp 1–10 | Cite as

Boundary-Value Problems for Loaded Pseudoparabolic Equations of Fractional Order and Difference Methods of Their Solving

  • M. Kh. BeshtokovEmail author


The paper is devoted to local and nonlocal boundary-value problems for a loaded differential equation with variable coefficients and the Gerasimov-Kaputo fractional derivative. To solve the considered problems we obtain a priori estimates in differential and difference interpretations, from which follow the uniqueness and stability of solution with respect to initial data and the right-hand side, as well as convergence of a solution to the difference problem to a solution of the differential problem.

Key words

boundary-value problems a priori estimate loaded equations equation of pseudoparabolic type differential equation of fractional order Gerasimov-Kaputo fractional derivative 


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  1. 1.
    Nakhushev, A. M. “Loaded Equations and their Applications”, Differentsial’nye Uravneniya 19, No. 1, 86–94 (1983).MathSciNetzbMATHGoogle Scholar
  2. 2.
    Kanchukoev, V. Z. “Boundary-value Problems for the Third Order Equation of Mixed Hyprbolic-Parabolic Type”, Candidate’s Dissertation in Mathematics and Physics (Moscow, 1984).Google Scholar
  3. 3.
    Kanchukoev, V. ‘Z. “Boundary-Value Problems for Equations of Pseudo-Parabolic and Mixed Hyperbolic-Parabolic Types and Their Applications to Calculation of Heat and Mass Transfer in Soils”, in SAPR i ASPR v Melioratsii (Nal’chik, 1983).Google Scholar
  4. 4.
    Kochina, N. I. “The Regulation of the Level of the Subsoil Waters in Irrigation”, DAN SSSR 213, No. 1, 51–54 (1973).Google Scholar
  5. 5.
    Nahušev, A. M., Borisov, V. N. “Boundary Value Problems for Loaded Parabolic Equations and Their Applications to the Prediction of Ground Water Level”, Differencial’nye Uravnenija 13, No. 1, 105–110 (1977).MathSciNetGoogle Scholar
  6. 6.
    Beshtokov, M. Kh. “To Boundary-Value Problems for Degenerating Pseudoparabolic Equations With Gerasimov-Caputo Fractional Derivative”, Russian Mathematics 62, No. 10, 1–14 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Samko, S. G., Kilbas, A. A., Marichev, O. I. Integrals and Derivatives of Fractional Order and Their Certain Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].zbMATHGoogle Scholar
  8. 8.
    Samarskii, A. A. Theory of Difference Schemes (Nauka, Moscow, 1983) [in Russian].Google Scholar
  9. 9.
    Alikhanov, A. A. “A Priori Estimates for Solutions of Boundary Value Problems for Equations of Fractional Order”, Differ. Equ. 46, No. 5, 660–666 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Alikhanov, A. A. “A New Difference Scheme for the Time Fractional Diffusion Equation”, J. Comput. Phys. 280, 424–438 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Voevodin, A. F., Shugrin, S. M. Numeric Methods of Calculation of One-Dimensional Systems (Nauka, SO RAN SSSR, Novosibirsk, 1981) [in Russian].zbMATHGoogle Scholar

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institite of applied mathematics and automation KBSC RASNalchikRussia

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