Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 111–118. ISSN 2079-6641
MSC 26A33
Research Article
Inverse problem for McKendrick von Foerster equation with Caputo operator
F. M. Losanova
Institute of Applied Mathematics and Automation KBSC RAS, 360000, Nalchik, Shortanova str., 89A, Kabardino-Balkarian Republic, Russia
E-mail: losanovaf@gmail.com
Fractional integro-differentiation operators are widely used in the study of applied problems that study mathematical models of physical and geophysical processes in fractal media. The fractional order derivative is not local, which exhibits behavior with long-term memory. Due to this, the models of dynamical systems of fractional order are more accurate than integer ones. In this paper, we consider an inverse problem for a generalized mathematical model of a biological process that characterizes the dynamics of a population with an age structure. The generalization is defined by introducing a derivative of a fractional order in the sense of Caputo into the equation.
Key words: inverse problem, McKendrick von Foerster equations, fractional derivative, fertility equation.
DOI: 10.26117/2079-6641-2022-40-3-111-118
Original article submitted: 03.11.2022
Revision submitted: 02.12.2022
For citation. Losanova F. M. Inverse problem for McKendrick von Foerster equation with Caputo operator. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 111-118. DOI: 10.26117/2079-6641-2022-40-3-111-118
Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.
The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)
© Losanova F. M., 2022
References
- Malthus T. R. An Essay on the principe of population Johnson. London, 1788.
- Riznichenko G. Y. Lektsii po matematicheskim modelyam v biologii [Lectures on mathematical models in biology]. Izdatel’stvo RKHD, 2011. 560 (In Russian)
- McKendrik A. G. Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 1926, 44:1, 98–130.
- Von Foerster H. Some remarks on changing populations. In: F. Stohlman (Ed.), The Kinetics of Cellular proliferation. New York: Grune and Stratton, 1959, 382–407.
- Nakhushev A. M. Uravneniya matematicheskoy biologii [Equations of mathematical biology]. Moscow, Vyssh. shk., 1995, 301 (In Russian)
- Nakhushev A. M. Drobnoye ischisleniye i yego primeneniye [Дробное исчисление и его применение]. Moscow, Fizmatlit, 2003, 272 (In Russian)
- Pskhu A. V. Krayevaya zadacha dlya differentsial’nogo uravneniya s chastnymi proizvodnymi drobnogo poryadka. Izvestiya KBNTS RAN, 2002, 1(8), 76–78 (In Russian)
- Mamchuev M. O. Krayevaya zadacha dlya uravneniya pervogo poryadka s chastnoy proizvodnoy drobnogo poryadka s peremennymi koeffitsiyentami. Doklady AMAN, 2009, 11:1, 32–35 (In Russian)
- Mamchuev M. O. Zadacha Koshi v nelokal’noy postanovke dlya uravneniya pervogo poryadka s chastnoy proizvodnoy drobnogo poryadka s peremennymi koeffitsiyentami. Doklady AMAN, 2009, 11:2, 21–24(In Russian)
- Pskhu A. V. On a boundary value problem for a fractional partial differential equation in a domain with curvilinear boundary, Differential Equations, 2015, 51:8, DOI: 10.1134/S001226611508011X.
- Kaygermazov A. A., Kudayeva F. Kh. Statsionarnyye sostoyaniya obobshchen-noy populyatsionnoy modeli Veybulla. Yuzhno – Sibirskiy nauchnyy vestnik, 2015, 17:1(19), 10–14 (In Russian)
- Kovaleva M. O. Vozrastnaya struktura izolirovannoy populyatsii. Sbornik trudov I Vserossiyskogo kongressa molodykh uchenykh. Spb: NIU ITMO, 2012, 15–20 (In Russian)
- Losanova F. M., Kenetova R. O. Nelokal’naya zadacha dlya obobshchennogo uravneniya Mak-Kendrika – fon Ferstera s operatorom Kaputo. Nelineynyy mir, 2018, 16:1, 49–53 (In Russian)
- Kenetova R. O., Losanova F. M. O nelokal’noy krayevoy zadache dlya obobshchennogo uravneniya Makkendrika-Fon Ferstera. Izvestiya KBNTS RAN, 2017, 2(76), 49–53 (In Russian)
- Pskhu A. V. Uravneniya v chastnykh proizvodnykh drobnogo poryadka [Fractional Partial Differential Equations]. Moscow, Nauka, 2005, 199 (In Russian)
Losanova Fatima Mukhamedovna – Researcher, Laboratory of Synergetic Problems, Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center, Russian Academy of Sciences, Nalchik, Kabardino-Balkarian Republic, Russia, ORCID 0000-0002-6342-7162.