{"id":6010,"date":"2026-01-21T11:29:07","date_gmt":"2026-01-21T11:29:07","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=6010"},"modified":"2026-04-13T13:10:09","modified_gmt":"2026-04-13T12:10:09","slug":"27-6-2-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-6-2-en\/","title":{"rendered":"27.6.2 En"},"content":{"rendered":"\n

Nonlocal boundary value problem for the McKendrick \u2013 von Foerster loaded equation of fractional-order<\/strong><\/h1>\n\n\n\n

F.M. Losanova, R.O. Kenetova<\/strong><\/p>\n\n\n\n

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Upload the full text<\/strong><\/strong><\/p>\n\n\n\n

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Abstract<\/strong>.<\/strong> <\/em>The paper considers McKendrick\u2013von Foerster loaded equation of fractional-order.
Aim<\/strong>. The study aims to demonstrate the existence of a unique solution ‘loaded equation’ within \u03a9, contingent upon satisfaction of regularity conditions.
Research methods<\/strong>. The convergence towards a solution was achieved via a reduction to a Volterra integral equation system, specifically of the second order. Employed the fractional calculus operator.
Results<\/strong>. Given the McKendrick \u2013 von Foerster loaded equation of fractional-order, the existence and uniqueness of a solution to a nonlocal boundary value problem is proven. An explicit representation of the solution is derived, expressed as integral equations.
Conclusion<\/strong>. The derived results facilitate mathematical modeling, specifically applied to population dynamics. Consider age-structured populations and incorporate diffusion phenomena exhibiting memory effects, formally representable via fractional-order derivatives. The derived theorems augment the axiomatic foundation for analyzing said differential equations, enabling further investigation in mathematical biology and the theory of integro-differential equations.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/em><\/strong> Gerasimov \u2013 Caputo derivative, loaded equation, McKendrick \u2013 von Foerster equations, Wright function, fractional order equations<\/p>\n\n\n\n

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For citation<\/strong>.<\/strong> Losanova F.M., Kenetova R.O. Nonlocal boundary value problem for the McKendrick \u2013 von Foerster loaded equation of fractional-order. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2025. Vol. 27. No. 6. Pp. 24\u201329. DOI: 10.35330\/1991-6639-2025-27-6-24-29<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Nakhushev A.M. Drobnoe ischislenie i ego primenenie [Fractional calculus and its applications]. Moscow: FIZMATLIT, 2003. 272 p. EDN: UGLEPD. (In Russian)<\/li>\n\n\n\n
  2. Nakhushev A.M. Uravneniya matematicheskoy biologii [Equations of mathematical biology]. Moscow: Vysshaya shkola, 1995. 301 p. EDN: PDBBNB. (In Russian)<\/li>\n\n\n\n
  3. Pskhu A.V. Boundary value problem for fractional partial differential equation. News of the Kabardino-Balkarian Scientific Center of RAS. 2002. No. 1(8). Pp. 76\u201378. EDN: VOVONL.
    (In Russian)<\/li>\n\n\n\n
  4. Mamchuev M.O. Boundary value problem for a first-order partial differential equation of fractional order with variable coefficients. Adyghe Int. Sci. J. 2009. Vol. 11. No. 1. Pp. 32\u201335. EDN: OHVXZT. (In Russian)<\/li>\n\n\n\n
  5. Mamchuev M.O. Cauchy problem in a nonlocal statement for a first-order partial differential equation of fractional order with variable coefficients. Adyghe Int. Sci. J. 2009. Vol. 11. No. 2. Pp. 21\u201324. EDN: OHLUYD. (In Russian)<\/li>\n\n\n\n
  6. Pskhu A.V. On a boundary value problem for a partial differential equation of fractional order in a domain with a curvilinear boundary. Differential Equations. 2015. Vol. 51. No. 8.
    Pp. 1076\u20131082. DOI: 10.1134\/S0374064115080117. (In Russian)<\/li>\n\n\n\n
  7. Kaygermazov A.A., Kudayeva F.Kh. Steady states of the generalized Weibull population model. South-Siberian Scientific Bulletin. 2015. Vol. 17. No. 1(19). mart. Pp. 10\u201314. EDN:
    TPEXPD. (In Russian)<\/li>\n\n\n\n
  8. Losanova F.M., Kenetova R.O. Nonlocal problem for the generalized McKendrick \u2013 von Foerster equation with the Caputo operator. Nonlinear World. 2018. Vol. 16. No. 1. Pp. 49\u201353. EDN: YQLELZ. (In Russian)<\/li>\n\n\n\n
  9. Losanova F.M. Inverse problem for McKendrick von Foerster equation with Caputo operator. Vestnik KRAUNC. Fiz.-mat. nauki. 2022. Vol. 40. No. 3. Pp. 111\u2013118. DOI:
    10.26117\/2079-6641-2022-40-3-111-118. (In Russian)<\/li>\n\n\n\n
  10. Losanova F.M., Kenetova R.O. Boundary value problem for the loaded McKendrick \u2013 von Foerster equation of fractional order. Adyghe Int. Sci. J. 2023. Vol. 23. No. 4. Pp. 28\u201333.
    DOI: 10.47928\/1726-9946-2023-23-4-28-33. EDN: UUZSAY. (In Russian)<\/li>\n\n\n\n
  11. Pskhu A.V. Uravneniya v chastnykh proizvodnykh drobnogo poryadka [Fractional Partial Differential Equations]. Moscow: Nauka, 2005. 199 p. EDN: QJPLZX. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong>s<\/summary>\n
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    Fatima M. Losanova,<\/strong> Researcher, Laboratory of Synergetic Problems, Institute of Applied Mathematics and Automation \u2013 branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    89 A, Shortanov street, Nalchik, 360000, Russia;
    losanovaf@gmail.com, ORCID: https:\/\/orcid.org\/0000-0002-6342-7162, SPIN-code: 8328-6335
    Raisa O. Kenetova<\/strong>, Candidate of Physics and Mathematics, Head of Laboratory of Synergetic Problems, Institute of Applied Mathematics and Automation \u2013 branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    89 A, Shortanov street, Nalchik, 360000, Russia;
    kenetova_r@mail.ru, SPIN-code: 8888-9163<\/p>\n\n\n\n

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

    Nonlocal boundary value problem for the McKendrick \u2013 von Foerster loaded equation of fractional-order F.M. Losanova, R.O. Kenetova Upload the full text Abstract. The paper considers McKendrick\u2013von Foerster loaded equation of fractional-order.Aim. The study aims to demonstrate the existence of a unique solution ‘loaded equation’ within \u03a9, contingent upon satisfaction of regularity conditions.Research methods. The […]<\/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-6010","page","type-page","status-publish","hentry"],"yoast_head":"\n27.6.2 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\/27-6-2-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"27.6.2 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=\"Nonlocal boundary value problem for the McKendrick \u2013 von Foerster loaded equation of fractional-order F.M. Losanova, R.O. Kenetova Upload the full text Abstract. The paper considers McKendrick\u2013von Foerster loaded equation of fractional-order.Aim. The study aims to demonstrate the existence of a unique solution ‘loaded equation’ within \u03a9, contingent upon satisfaction of regularity conditions.Research methods. 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Losanova, R.O. Kenetova Upload the full text Abstract. The paper considers McKendrick\u2013von Foerster loaded equation of fractional-order.Aim. The study aims to demonstrate the existence of a unique solution ‘loaded equation’ within \u03a9, contingent upon satisfaction of regularity conditions.Research methods. 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