{"id":1911,"date":"2025-05-09T07:49:50","date_gmt":"2025-05-09T06:49:50","guid":{"rendered":"http:\/\/newskbncran.ru\/?page_id=1911"},"modified":"2026-03-26T10:08:13","modified_gmt":"2026-03-26T10:08:13","slug":"26-1-7-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/26-1-7-en\/","title":{"rendered":"26.1.7-en"},"content":{"rendered":"\n

Boundary value problem for loaded parabolic equations<\/strong>of fractional order<\/strong><\/h1>\n\n\n\n

M.M. Karmokov, F.M. Nakhusheva, M.Kh. Abregov<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n\n\n\n

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Abstract<\/em>.<\/strong> The article considers the second boundary value problem for a loaded parabolic equation with a fractional Riemann \u2013 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.<\/p>\n\n\n\n

Keywords<\/em>:<\/strong> boundary value problems, parabolic equations, fractional integro-differentiation operator, loaded equation, regular solution<\/p>\n\n\n\n

For citation<\/strong>. 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.<\/em> <\/strong>2024. Vol. 26. No. 1. Pp. 69\u201377. DOI: 10.35330\/1991-6639-2024-26-1-69<\/p>\n\n\n\n

References<\/strong><\/summary>\n
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  1. Nakhushev A.M. Nagruzhennyye uravneniya i ikh primeneniye [Loaded equations and their application]. Moscow: Nauka, 2012. 232 p. (in Russian)<\/li>\n\n\n\n
  2. Nakhushev A.M. Uravneniya matematicheskoy biologii [Equations of mathematical biology]. Moscow: Vysshaya shkola, 1995. 301 p. (in Russian)<\/li>\n\n\n\n
  3. Nakhushev A.M. On the Darboux problem for a degenerate loaded second-order integrodifferential equation. Differential equations. 1976. Vol. 12. No. 1. Pp. 103\u2013108. (in Russian)<\/li>\n\n\n\n
  4. Dikinov Kh.B., Kerefov A.A., Nakhushev A.M. On a boundary value problem for the loaded equation of thermal conductivity. Differential equations. 1976. Vol. 12. Pp. 177\u2013179. (in Russian)<\/li>\n\n\n\n
  5. Karmokov M.M. Lokal\u2019nye i nelokal\u2019nye kraevye zadachi dlya razryvno-nagruzhennykh parabolicheskikh uravneniy<\/em> [Local and non-local boundary value problems for discontinuously loaded parabolic equations]. Kand. dis. Nalchik, 1990. 86 p. (in Russian)<\/li>\n\n\n\n
  6. Pskhu A.V. Uravneniya v chastnykh proizvodnykh drobnogo poryadka<\/em> [Partial differential equations of fractional order]. Moscow: Nauka, 2005. 199 p. (in Russian)<\/li>\n\n\n\n
  7. Gekkieva S.Kh. Mixed boundary value problems for the loaded diffusion-wave equation. Nauchnye vedomosti Belgorodskogo gosudanstiennogo universiteta. Seriya: Matematika. Fizika<\/em> [Scientific Bulletin of Belgorod Stade University. Senes: Mathemaitics. Physics]. 2016. Vol. 42. No. 6 (227). Pp. 32\u201335. (in Russian)<\/li>\n\n\n\n
  8. Nakhusheva F.M., Lafisheva M.M., Karmokov M.M., Dzhankulaeva M.A. A numerical method for solving a boundary value problem for a parabolic equation with a fractional time derivative with a concentrated heat capacity. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2018. No. 5(85). Pp. 34\u201343. (in Russian)<\/li>\n\n\n\n
  9. Beshtokov M.Kh., Vodakhova V.A., Isakova M.M. Approximate solution of the first boundary value problem for the loaded heat equation. Matematicheskaya fizika i komp\u2019yuternoe modelirovanie <\/em>[Mathematical physics and computer modeling]. 2023. Vol. 26. No. 4. Pp. 5\u201317. (in Russian)<\/li>\n\n\n\n
  10. Friedman A. Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa<\/em> [Partial Differential Equations of Parabolic Type]. Moscow: Mir, 1968. 427 p. (in Russian)<\/li>\n<\/ol>\n\n\n\n

    <\/p>\n<\/details>\n\n\n\n

    Information about the authors<\/strong><\/summary>\n

    Mukhamed M. Karmokov<\/strong>, 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<\/strong>, 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<\/strong>, 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<\/p>\n\n\n\n

    <\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"

    Boundary value problem for loaded parabolic equationsof fractional order M.M. Karmokov, F.M. Nakhusheva, M.Kh. Abregov Upload the full text Abstract. The article considers the second boundary value problem for a loaded parabolic equation with a fractional Riemann \u2013 Liouville integro-differentiation operator. The unambiguous solvability of the second boundary value problem is proved. Using the Green function method […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-1911","page","type-page","status-publish","hentry"],"yoast_head":"\n26.1.7-en - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/26-1-7-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"26.1.7-en - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Boundary value problem for loaded parabolic equationsof fractional order M.M. 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