Boundary value problem for loaded parabolic equationsof fractional order
M.M. Karmokov, F.M. Nakhusheva, M.Kh. Abregov
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Abstract. The article considers the second boundary value problem for a loaded parabolic equation with a fractional Riemann – Liouville integro-differentiation operator. The unambiguous solvability of the second boundary value problem is proved. Using the Green function method with the theory of the potential of a simple layer, the problem is reduced to a system of Volterra integral equations of the second kind.
Keywords: boundary value problems, parabolic equations, fractional integro-differentiation operator, loaded equation, regular solution
For citation. Karmokov M.M., Nakhusheva F.M., Abregov M.Kh. Boundary value problem for loaded parabolic equations of fractional order. News of the Kabardino-Balkarian Scientific Center of RAS. 2024. Vol. 26. No. 1. Pp. 69–77. DOI: 10.35330/1991-6639-2024-26-1-69
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Information about the authors
Mukhamed M. Karmokov, Candidate of physical and mathematical sciences, Associate Professor of the Department of applied mathematics and computer science, Kabardino-Balkarian State University
named after Kh. M. Berbekov;
360004, Russia, Nalchik, 173 Chernyshevsky street;
mkarmokov@yandex.ru, ORCID: https://orcid.org/0000-0001-5189-6538
Fatima M. Nakhusheva, Candidate of physical and mathematical sciences, Associate Professor of the Department of applied mathematics and computer science, Kabardino-Balkarian State University named after Kh. M. Berbekov;
360004, Russia, Nalchik, 173 Chernyshevsky street;
fatima-nakhusheva@mail.ru, ORCID: https://orcid.org/0000-0002-3750-1445
Mukhad Kh. Abregov, Candidate of physical and mathematical sciences, Associate Professor of the Department of applied mathematics and computer science, Kabardino-Balkarian State University named after Kh. M. Berbekov;
360004, Russia, Nalchik, 173 Chernyshevsky street;
ORCID: https://orcid.org/0009-0003-9592-4133