Adyghe Int. Sci. J. Vol. 24, No. 4. P. 91–100.
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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-91-100
EDN: OHUKVC
MATHEMATICS
| MSC 34B10 | Original Article |
A non-local problem for an ordinary
second-order differential equation
with the Nakhushev operator
Beslan Igorevich Efendiev
Candidate of Physical and Mathematical Sciences, Researcher Department of Fractional Calculus Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), ORCID: https://orcid.org/0000-0002-5730-2160, beslan_efendiev@mail.ru
Abstract. In this paper, we study an ordinary differential equation of the second order with the Nakhushev differentiation operator in the lower terms. The Nakhushev differentiation operator belongs to the class of continuously distributed differentiation operators. For this equation, a non-local boundary value problem with the Ilyin–Moiseev condition of the first kind is considered. The Ilyin–Moiseev condition of the first kind connects the value of the desired function at the right end of the interval, where the equation is set, with the values of the desired function at the inner (several) points of the interval. The method of the Green function is used to find a solution to the problem under study, the corresponding Green function is constructed and its properties are studied.
Keywords: fractional Riemann–Liouville integral, fractional Riemann–Liouville derivative, Nakhushev differentiation operator, nonlocal problem, Ilyin–Moiseev condition.
Funding. This work was carried out within the framework of the state assignment of the Ministry of Education and Science of the Russian Federation under the project: Investigation of boundary value problems for equations with generalised fractional differentiation operators and their application to mathematical modelling of physical and socio-economic processes (1021032424223-6).
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.
For citation. Efendiev B. I. A non-local problem for an ordinary second-order differential equation with the Nakhushev operator. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 91–100.
DOI: https://doi.org/10.47928/1726-9946-2024-24-4-91-100; EDN: OHUKVC
Submitted 05.12.2024; approved after reviewing 16.12.2024; accepted for publication 16.12.2024.
© Efendiev B. I., 2024
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