Adyghe Int. Sci. J. Vol. 24, No 3. P. 11–18.
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DOI: https://doi.org/10.47928/1726-9946-2024-24-3-11-18
EDN: CRJZHB
MATHEMATICS
| MSC 34A08, 34B05 | Original Article |
On the generalized boundary value problem
for a linear ordinary delay differential equation
with Dzhrbashyan–Nersesyan derivative
Mazhgikhova Madina Gumarovna
Candidate of Physical and Mathematical Sciences, Junior Researcher of Department of Fractional Calculus, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 A Shortanova St., Nalchik, Russia), ORCID: https://orcid.org/0000-0001-7612-8850, madina.mazhgihova@yandex.ru
Abstract. In this paper, a solution to a boundary value problem with generalized Sturm-type conditions for a linear ordinary delay differential equation with the Dzhrbashyan–Nersesyan fractional differentiation operator of arbitrary order, is constructed. For the problem under study, an explicit representation of the solution and a condition for unique solvability are obtained. An existence and uniqueness theorem is formulated. The solution to the problem is written out in terms of a special function W\nu (t), which is defined in terms of the generalized Mittag-Leffler function.
Keywords: fractional differential equation, fractional derivative, Dzhrbashyan–Nersesyan derivative, delay differential equation, generalized boundary conditions, Sturm-type conditions, generalized Mittag-Leffler function.
Funding. The work was not carried out within the framework of funds.
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. M. G. Mazhgikhova On the generalized boundary value problem for a linear ordinary delay differential equation with Dzhrbashyan–Nersesyan derivative. Adyghe Int. Sci. J. 2024. Vol. 24, No. 3. Pp. 11–18. DOI: https://doi.org/10.47928/1726-9946-2024-24-3-11-18; EDN: CRJZHB
The author has read and approved the final version of the manuscript.
Submitted 14.09.2024; approved after reviewing 23.09.2024; accepted for publication 24.09.2024.
© Mazhgikhova M. G., 2024
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