Mixed boundary value problem for one discontinuously loaded parabolic equation
- Authors: Karmokov M.M.1, Kerefov M.A.1, Gekkieva S.K.2
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Affiliations:
- Kabardino-Balkarian State University named after Kh.M. Berbekov
- Institute of Applied Mathematics and Automation - branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
- Issue: Vol 27, No 6 (2025)
- Pages: 13-23
- Section: Математика и механика
- Submitted: 29.01.2026
- Published: 02.02.2026
- URL: https://journals.rcsi.science/1991-6639/article/view/378579
- DOI: https://doi.org/10.35330/1991-6639-2025-27-6-13-23
- EDN: https://elibrary.ru/AMSYXU
- ID: 378579
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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-differen- tiation 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.
About the authors
Mukhamed M. Karmokov
Kabardino-Balkarian State University named after Kh.M. Berbekov
Email: mkarmokov@yandex.ru
ORCID iD: 0000-0001-5189-6538
SPIN-code: 1771-6984
Candidate of Physics and Mathematics, Associate Professor, Department of Applied Mathematics and Computer Science
Russian Federation, 173, Chernyshevsky street, Nalchik, 360004, RussiaMarat A. Kerefov
Kabardino-Balkarian State University named after Kh.M. Berbekov
Email: kerefov@mail.ru
ORCID iD: 0000-0002-7442-5402
SPIN-code: 1424-6720
Candidate of Physics and Mathematics, Associate Professor, Department of Applied Mathematics and Computer Science
Russian Federation, 173, Chernyshevsky street, Nalchik, 360004, RussiaSakinat Kh. Gekkieva
Institute of Applied Mathematics and Automation - branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
Author for correspondence.
Email: gekkieva_s@mail.ru
ORCID iD: 0000-0002-2135-2115
SPIN-code: 6711-3471
Candidate of Physical and Mathematical Sciences, Leading Researcher, Department of Computational Methods
Russian Federation, 89 A, Shortanov street, Nalchik, 360000, RussiaReferences
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