Adyghe Int. Sci. J. Vol. 24, No. 4. P. 39–46.
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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-39-46
EDN: ESBHPN
MATHEMATICS
MSC 35A08, 35A09, 34A08 | Original Article |
Boundary value problem for the loaded fractional telegraph equation
with Gerasimov–Caputo derivatives
Fatima Mukhamedovna Losanova
Researcher, Laboratory of Synergetic Problems, Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), ORCID https://orcid.org/0000-0002-6342-7162, losanovaf@gmail.com
Raisa Osmanovna Kenetova
Candidate of Physical and Mathematical Sciences, Head of Laboratory of Synergetic Problems, Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), kenetova_r@mail.ru
Abstract. The first boundary value problem in the rectangular region for the loaded fractional telegraph equation with Gerasimov–Caputo derivatives is investigated. By the method of reduction to the Volterra integral equation of the 2nd kind the solution of the problem is found. The existence and uniqueness theorem of the solution is proved.
Keywords: first boundary value problem, loaded fractional telegraph equation, Gerasimov–Caputo derivative, Green’s function, Wright’s function.
Funding. This work was carried out within the framework of 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. Losanova F. M., Kenetova R. O. Boundary value problem for the loaded fractional telegraph equation with Gerasimov–Caputo derivatives. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 39–46.
DOI: https://doi.org/10.47928/1726-9946-2024-24-4-39-46; EDN: ESBHPN
Submitted 06.12.2024; approved after reviewing 13.12.2024; accepted for publication 16.12.2024.
© Losanova F. M., Kenetova R. O., 2024
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