Nonlocal boundary value problem for the McKendrick - von Foerster loaded equation of fractional-order
- Authors: Losanova F.M.1, Kenetova R.O.1
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Affiliations:
- 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: 24-29
- Section: Математика и механика
- Submitted: 29.01.2026
- Published: 02.02.2026
- URL: https://ogarev-online.ru/1991-6639/article/view/378590
- DOI: https://doi.org/10.35330/1991-6639-2025-27-6-24-29
- EDN: https://elibrary.ru/BHXCHC
- ID: 378590
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Abstract
The paper considers McKendrick–von Foerster loaded equation of fractional-order.
Aim. The study aims to demonstrate the existence of a unique solution 'loaded equation' within Ω, contingent upon satisfaction of regularity conditions.
Research methods. 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. Given the McKendrick – 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. 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.
About the authors
Fatima M. Losanova
Institute of Applied Mathematics and Automation - branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
Email: losanovaf@gmail.com
ORCID iD: 0000-0002-6342-7162
SPIN-code: 8328-6335
Researcher, Laboratory of Synergetic Problems
Russian Federation, 89 A, Shortanov street, Nalchik, 360000, RussiaRaisa O. Kenetova
Institute of Applied Mathematics and Automation - branch of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
Author for correspondence.
Email: kenetova_r@mail.ru
SPIN-code: 8888-9163
Candidate of Physics and Mathematics, Head of Laboratory of Synergetic Problems
Russian Federation, 89 A, Shortanov street, Nalchik, 360000, RussiaReferences
- Nakhushev A.M. Drobnoe ischislenie i ego primenenie [Fractional calculus and its applications]. Moscow: FIZMATLIT, 2003. 272 p. EDN: UGLEPD. (In Russian)
- Nakhushev A.M. Uravneniya matematicheskoy biologii [Equations of mathematical biology]. Moscow: Vysshaya shkola, 1995. 301 p. EDN: PDBBNB. (In Russian)
- 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. 76–78. EDN: VOVONL. (In Russian)
- 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. 32–35. EDN: OHVXZT. (In Russian)
- 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. 21–24. EDN: OHLUYD. (In Russian)
- 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. 1076–1082. doi: 10.1134/S0374064115080117. (In Russian)
- 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. 10–14. EDN: TPEXPD. (In Russian)
- Losanova F.M., Kenetova R.O. Nonlocal problem for the generalized McKendrick – von Foerster equation with the Caputo operator. Nonlinear World. 2018. Vol. 16. No. 1. Pp. 49–53. EDN: YQLELZ. (In Russian)
- Losanova F.M. Inverse problem for McKendrick von Foerster equation with Caputo operator. Vestnik KRAUNC. Fiz.-mat. nauki. 2022. Vol. 40. No. 3. Pp. 111–118. doi: 10.26117/2079-6641-2022-40-3-111-118. (In Russian)
- Losanova F.M., Kenetova R.O. Boundary value problem for the loaded McKendrick – von Foerster equation of fractional order. Adyghe Int. Sci. J. 2023. Vol. 23. No. 4. Pp. 28–33. doi: 10.47928/1726-9946-2023-23-4-28-33. EDN: UUZSAY. (In Russian)
- Pskhu A.V. Uravneniya v chastnykh proizvodnykh drobnogo poryadka [Fractional Partial Differential Equations]. Moscow: Nauka, 2005. 199 p. EDN: QJPLZX. (In Russian)
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