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The journal was founded in 1998, 6 issues per year
ISSN 1991-6639 (print),

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Mixed boundary value problem for one discontinuously loaded parabolic equation

M.M. Karmokov, M.A. Kerefov, S.Kh. Gekkieva

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Abstract: This article is devoted to current issues in the theory of partial differential equations related to the study of boundary value problems for loaded parabolic equations with a fractional integro-differentiation operator, which are of interest not only for the advancement of this specific theory, but also for their numerous applications.
Aim. The study is to prove the unique solvability of a mixed boundary value problem for a discontinuously loaded parabolic equation with the Riemann–Liouville fractional derivative.
Research methods. The study employs the Green’s function method, simple layer potential theory, and fractional calculus theory.
Results. This paper demonstrates the unique solvability of a mixed boundary value problem for a loaded fractional-order parabolic equation.
Conclusion. The results obtained are significant for the development of the theory of boundary value problems for partial differential equations of fractional order, including loaded parabolic equations; they are also relevant for mathematical modeling of various processes and systems with distributed parameters and fractal structures.

Keywords: boundary value problems, parabolic equations, fractional integro-differentiation operator, loaded equation, regular solution

For citation. Karmokov M.M., Kerefov M.A., Gekkieva S.Kh. Mixed boundary value problem for one discontinuously loaded parabolic equation. News of the Kabardino-Balkarian Scientific Center of RAS. 2025. Vol. 27. No. 6. Pp. 13–23. DOI: 10.35330/1991-6639-2025-27-6-13-23

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Information about the authors

Mukhamed M. Karmokov, Candidate of Physics and Mathematics, Associate Professor, Department of Applied Mathematics and Computer Science, Kabardino-Balkarian State University named after Kh.M. Berbekov;
173, Chernyshevsky street, Nalchik, 360004, Russia;
mkarmokov@yandex.ru, ORCID: https://orcid.org/0000-0001-5189-6538, SPIN-code: 1771-6984
Marat A. Kerefov, Candidate of Physics and Mathematics, Associate Professor, Department of Applied Mathematics and Computer Science, Kabardino-Balkarian State University named after Kh.M. Berbekov;
173, Chernyshevsky street, Nalchik, 360004, Russia;
kerefov@mail.ru, ORCID: https://orcid.org/0000-0002-7442-5402, SPIN-code: 1424-6720
Sakinat Kh. Gekkieva, Candidate of Physical and Mathematical Sciences, Leading Researcher, Department of Computational Methods, Institute of Applied Mathematics and Automation – branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
89 A, Shortanov street, Nalchik, 360000, Russia;
gekkieva_s@mail.ru, ORCID: https://orcid.org/0000-0002-2135-2115, SPIN-code: 6711-3471

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