Adyghe Int. Sci. J. Vol. 25, No. 1. Pp. 19–29.
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DOI: https://doi.org/10.47928/1726-9946-2025-25-1-19-29
EDN: ROOGAO
MATHEMATICS
| MSC 34B10 | Original Article |
A non-local problem of the second king for an ordinary second-order
differential equation with the Nakhushev differentiation 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 second-order differential equation with the Nakhushev 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 second kind is considered. The Ilyin-Moiseev condition of the second kind connects the value of the first derivative of the desired function at the right end of the interval, where the equation is set, with the values of the first derivative of the desired function at the inner (several) points of the interval. The Green function method is used to find a solution to the problem under study, construct the corresponding Green function, and study its properties.
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: Boundary value problems for equations and systems with fractional and distributed order differentiation operators and their applications (125031904191-2).
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 of the second king for an ordinary second-order differential equation with the Nakhushev differentiation operator. Adyghe Int. Sci. J. 2025. Vol. 25, No. 1. Pp. 19–29.
DOI: https://doi.org/10.47928/1726-9946-2025-25-1-19-29; EDN: ROOGAO
Submitted 20.03.2025; approved after reviewing 01.04.2025; accepted for publication 01.04.2025.
© Efendiev B. I., 2025
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