Adyghe Int. Sci. J. Vol. 24, No. 1. P. 36–44. 

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DOI: https://doi.org/10.47928/1726-9946-2024-24-1-36-44
EDN: RMXQDU

MATHEMATICS

MSC 32А10; 32А37

Original Article

On some formulas for fractional integration of one Fox function with five parameters

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

Abstract. The study obtained Riemann – Liouville and Erdelyi – Kober formulas for fractional integration of five-parameter special Fox function. The paper gives an integral representation of the function under consideration in terms of the Mellin – Barnes integral, conditions for absolute convergence, and asymptotic expansions both for large and small values of the argument. We obtained the formulas proved, using the above integral representation and known power rules for integration. For partial parameters, we got some well-known elementary and special functions.

Keywords: Fox function, Riemann – Liouville fractional integration, Erdelyi – Kober fractional integration.

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. Khushtova F. G. On some formulas for fractional integration of one Fox function with five parameters. Adyghe Int. Sci. J. 2024. Vol. 24, No. 1. Pp. 36–44. DOI: https://doi.org/10.47928/1726-9946-2024-24-1-36-44; EDN: RMXQDU.

Submitted 11.03.2024; approved after reviewing 20.03.2024; aeeepted for publication 22.03.2024.

© Khushtova F. G., 2024

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