Adyghe Int. Sci. J. Vol. 25, No. 1. Pp. 11–18.
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DOI: https://doi.org/10.47928/1726-9946-2025-25-1-11-18
EDN: OXOAFG
MATHEMATICS
| MSC 33E12; 35K20; 44A10 | Original Article |
On the equivalence of representations
of Green’s functions
of boundary value problems
for the fractional diffusion equation
Fatima Gidovna Khushtova
Candidate of Physical and Mathematical Sciences, Researcher of Department of Fractional Calculus, Institute of Applied Mathematics and Automation of KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), ORCID: http://orcid.org/0000-0003-4088-3621, khushtova@yandex.ru
Abstract. In this paper, formulas for the integral Stankovich transforms of some elementary and special functions that are important in the theory of boundary value problems of mathematical physics are obtained. To prove the obtained formulas, integral representations, or expansions in power series, of the functions to which the transforms are applied are usedIn this paper, proves the equivalence of two expansions in series in some special functions. This paper is a continuation of the previously proven equivalence of two forms of the Green function of the first boundary value problem in a rectangular domain for the fractional diffusion equation.
Keywords: Green function, Wright function, Mittag–Leffler type function, Fourier series.
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. Khushtova F. G. On the equivalence of representations of Green’s functions of boundary
value problems for the fractional diffusion equation. Adyghe Int. Sci. J. 2025. Vol. 25, No. 1. Pp. 11–18.
DOI: https://doi.org/10.47928/1726-9946-2025-25-1-11-18; EDN: OXOAFG
Submitted 20.03.2025; approved after reviewing 07.04.2025; accepted for publication 07.04.2025.
© Khushtova F. G., 2025
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