Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 52. no. 3. P. 63 – 74. ISSN 2079-6641

MATHEMATICS
https://doi.org/10.26117/2079-6641-2025-52-3-63-74
Research Article
Full text in Russian
MSC 45A05, 26A33

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Fractional Integral Equation with Involution

L. M. Eneeva^{\ast}

Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center RAS,
360000, Nalchik, Shortanova st., 89 A, Russia

Abstract. This paper considers a linear integral equation containing a fractional integration operator in the Riemann–Liouville sense and an involution operator. This equation belongs to the class of functional integral equations that arise in the study of boundary value problems for fractional differential equations containing a composition of left- and right-hand fractional derivatives. Such equations, in turn, form the basis of an effective analytical framework for describing dissipative oscillatory systems and, in particular, are of great importance in solving problems of mathematical modeling of various physical and geophysical processes. In this paper, the solvability of the functional integral equation under study is reduced to the solvability of a Fredholm integral equation of the second kind with fractional integration operators. To achieve this, we analyze a special functional equation and find its inversion formula. The main results of the paper are formulated as a theorem, specifying sufficient conditions on the input parameters of the problem that ensure the unique solvability of the equation under consideration.

Key words: fractional integral equation, Riemann-Liouville integral, involution.

Received: 06.11.2025; Revised: 07.11.2025; Accepted: 09.11.2025; First online: 11.11.2025

For citation. Eneeva L. M. Fractional integral equation with involution. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 52: 3, 63-74. EDN: EOPADJ. https://doi.org/10.26117/2079-6641-2025-52-3-63-74.

Funding. The work was carried out within the framework of the state assignment of the IPMA KBSC RAS (reg. No. 125031904215-5).

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. Author is solely responsible for providing the final version of the article in print.

^{\ast}Correspondence: E-mail: eneeva72@list.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Eneeva L. M., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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