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Vol. 24, No. 4. P. 19–27

Adyghe Int. Sci. J. Vol. 24, No. 4. P. 19–27. 

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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-19-27
EDN: LIGAIK

MATHEMATICS

MSC 34A08, 34B05 Original Article

Non-local boundary value problem

for an ordinary fractional differential equation with the Dzhrbashyan–Nersesyan operator

Fatima Takhirovna Bogatyreva
unior 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/0000-0003-1765-066X, fatima_bogatyreva@bk.ru

Abstract. In this paper, we study a nonlocal boundary value problem with integral displacement for an ordinary differential equation of fractional order containing the Dzhrbashyan–Nersesyan operator. Equations containing such operators are more complex and interesting to study than classical differential equations, due to some features of the Dzhrbashyan–Nersesyan operator.
Using methods of mathematical analysis and the theory of fractional equations, an explicit representation of the solution to this problem was constructed. The resulting solution is expressed through the Mittag-Leffler function, which is a generalization of the exponential function to the case of fractional powers.

Keywords: fractional differential equation, Riemann–Liouville fractional derivative, Dzhrbashyan–Nersesyan derivative, nonlocal boundary value problem.

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. Bogatyreva F. T. Non-local boundary value problem for an ordinary fractional differential equation with the Dzhrbashyan–Nersesyan operator. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 19–27.
DOI: https://doi.org/10.47928/1726-9946-2024-24-4-19-27; EDN: LIGAIK

Submitted 06.12.2024; approved after reviewing 12.12.2024; accepted for publication 13.12.2024.

© Bogatyreva F. T., 2024

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