Adyghe Int. Sci. J. Vol. 24, No. 4. P. 62–71.
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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-62-71
EDN: YYFXTG
MATHEMATICS
MSC 35L10 | Original Article |
Problem with non-local internal
and boundary conditions
for a fractional diffusion-wave equation
Mamchuev Murat Osmanovich
Doctor of Physical and Mathematical Sciences, Head of the Fractional Calculus Department, Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.),; Professor of the Department of Computer Technologies and Artificial Intelligence, Kabardino-Balkarian State University named after Kh. M. Berbekov, ORCID https://orcid.org/0000-0002-7986-456X, mamchuev@rambler.ru
Mashukov Musa Beslanovich
postgraduate student of the Scientific and Educational Center of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences (360002, Kabardino-Balkarian Republic, Nalchik, 2 Balkarova St.), musa.mashukov.99@mail.ru
Abstract. The paper studies a fractional diffusion-wave equation with a fractional derivative in the sense of Garasimov–Caputo. In terms of integral operators associated with the fractional diffusion-wave equation, the necessary nonlocal conditions are written out, which connect the traces of the solution under study and its derivatives on the boundary of a rectangular region. Based on this property, the unique solvability of the problem with nonlocal internal and boundary conditions is proven. The solution is obtained in explicit form.
Keywords: fractional diffusion-wave equation, nonlocal problem, necessary nonlocal conditions, problem with integral conditions, fractional derivative of Gerasimov–Caputo.
Funding. The work was carried out within the framework of the programme «Priority 2030» and the state assignment of the Ministry of Education and Science of the Russian Federation under the project: Investigation of boundary value problems for equations with generalised fractional differentiation operators and their application to mathematical modelling of physical and socio-economic processes (1021032424223-6).
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The authors participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.
For citation. Mamchuev M. O., Mashukov M. B. Problem with non-local internal and boundary conditions for a fractional diffusion-wave equation. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 62–71.
DOI: https://doi.org/10.47928/1726-9946-2024-24-4-62-71; EDN: YYFXTG
Submitted 09.12.2024; approved after reviewing 16.12.2024; accepted for publication 16.12.2024.
© Mamchuev M. O., Mashukov M. B., 2024
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