Adyghe Int. Sci. J. Vol. 22, No 4. P. 11-17. ISSN 1726-9946

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DOI: https://doi.org/10.47928/1726-9946-2022-22-4-11-17

MATHEMATICS

MSC 34А08, 34В05

Original Article

Generalized Dirichlet problem for an ordinary delay differential equation with Dzhrbashyan – Nersesyan derivative

Mazhgikhova Madina Gumarovna
Junior Researcher of Department of Fractional Calculus, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 A Shortanova St., Nalchik, Russia), https://orcid.org/0000-0001-7612-8850, madina.mazhgihova@yandex.ru

Abstract. In recent decades, interest in the study of differential equations involving fractional derivatives has noticeably increased. This interest is due to the fact that the number of fields of science in which equations containing fractional derivatives arc used varies from biology and medicine to management theory, engineering, finance, as well as optics, physics and so on. In this paper, the generalized Dirichlet problem is investigated for a linear ordinary delay differential equation with Dzhrbashyan – Nersesyan fractional differentiation operator. A condition for unique solvability is obtained. The existence and uniqueness theorem to the solution is proved. The solution of the problem is written out in terms of the special function Wv (t), which is defined in terms of the generalized Mittag – Leffler function (Prabhakar function).

Keywords: fractional differential equation, fractional derivative, Dzhrbashyan-Ncrscsyan derivative, delay differential equation, Dirichlet problem, generalized boundary conditions, generalized Mittag – Leffler function

Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.

For citation. M. G. Mazhgikhova Generalized Dirichlet problem for an ordinary delay differential equation with Dzhrbashyan – Nersesyan derivative. Adyghe hit. Sei. J. 2022. Vol. 22, No. 4. P. 11-17.
DOI: https://doi.org/10.47928/1726-9946-2022-22-4-ll-17

The author has read and approved the final version of the manuscript.
Submitted 12.12.2022; approved after reviewing 19.12.2022; aeeepted for publication 20.12.2022

© Mazhgikhova M. G., 2022

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