Adyghe Int. Sci. J. Vol. 22, No 2. P. 34-40. ISSN 1726-9946

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DOI: https://doi.org/10.47928/1726-9946-2022-22-2-34-40

MATHEMATICS

MSC 32A10; 32A37

Original Article

On some properties of one special function

Fatima Gidovna Khushtova
Researcher of Department of Fractional Calculus, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 А Shortanova St., Nalchik, Russia), Ph.D., http://orcid.org/0000-0003-4088-3621, khushtova@yandex.ru

Abstract. In the paper, some properties of one particular case of the special Fox function are studied. In particular, an autotransformation formula and its integral representation for some parameters are obtained. The Mellin transform formula is given. In terms of the function under study, solutions to boundary value problems for a differential equation with a Bessel operator acting with respect to a spatial variable and a partial derivative of a fractional order with respect to a time variable were previously written out. When proving the results obtained, the well-known properties of the Euler gamma function, the Wright function, and the properties of the Mellin transform were used.

Keywords: Fox function, Wright function, Euler gamma function, Mellin transform, Mellin convolution

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

For citation. F.~G. Khushtova On some properties of one special function. Adyghe Int. Sci. J. 2022. Vol. 22, No. 2. P. 34–40. DOI: https://doi.org/10.47928/1726-9946-2022-22-2-34-40 

The author has read and approved the final version of the manuscript.
Submitted 24.06.2022; approved after reviewing 01.07.2022; accepted for publication 04.07.2022.

© Хуштова Ф. Г., 2022

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