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On Boundary Value Problems for Fractional-Order Differential Equations

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Abstract

The article is devoted to the study of boundary value problems for a fractional-order convection-diffusion equation with memory effect. We construct two-layer monotone schemes with weights of the second order accuracy with respect to the time and space variables. We prove the uniqueness and stability for the solution with respect to the initial data and right-hand side and also the convergence of the solution of the difference scheme to the solution of the corresponding differential problem.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automatization, Nal’chik, 360000, Russia

    M. Kh. Beshtokov

  2. North-Caucasus Federal University, Stavropol, 355017, Russia

    M. Kh. Beshtokov

  3. Medical College of Kabardino-Balkarian University, Nal’chik, 360000, Russia

    F. A. Erzhibova

Authors
  1. M. Kh. Beshtokov
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  2. F. A. Erzhibova
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Corresponding authors

Correspondence to M. Kh. Beshtokov or F. A. Erzhibova.

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Beshtokov, M.K., Erzhibova, F.A. On Boundary Value Problems for Fractional-Order Differential Equations. Sib. Adv. Math. 31, 229–243 (2021). https://doi.org/10.1134/S1055134421040015

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  • DOI: https://doi.org/10.1134/S1055134421040015

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