Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 64–71. ISSN 2079-6641

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MSC 26A33, 34B05

Research Article

Solution of a mixed boundary value problem for an equation with fractional derivatives with different origins

L. M. Eneeva

Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center RAS, 360000, Nalchik, Shortanova st., 89 A, Russia
E-mail: eneeva72@list.ru

A solution of a mixed boundary value problem for an ordinary differential equation of fractional order is constructed. The main part of the equation is a composition of left- and right-hand Riemann-Liouville and Caputo fractional differentiation operators. A representation of the solution of the problem under study is found,
and an estimate for the eigenvalues is also obtained.

Key words: fractional differential equation with different origins, mixed boundary value problem, Riemann-Liouville derivative, Caputo derivative.

DOI: 10.26117/2079-6641-2022-40-3-64-71

Original article submitted: 26.10.2022

Revision submitted: 23.11.2022

For citation. Eneeva L.M. Solution of a mixed boundary value problem for an equation with fractional derivatives with different origins. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40:3, 64-71. DOI: 10.26117/2079-6641-2022-40-3-64-71

Competing interests. The author declares that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author contributed to this article. The author is solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by the author.

Funding. The work was carried out within the framework of the state assignment (state registration number No. 122041800015-8)

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Eneeva L. M., 2022

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Eneeva Liana Magometovna – Ph. D. (Phys. & Math.), Senior Researcher at the Institute of Applied Mathematics and Automation of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, Nalchik, Russia, ORCID 0000-0003-2530-5022.

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