Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 221, Pages 63–70
DOI: https://doi.org/10.36535/0233-6723-2023-221-63-70 (Mi into1130) 		 
First boundary-value problem for the Aller–Lykov equation with the Caputo fractional derivative

M. A. Kerefova, S.Kh. Gekkievaa, B. M. Kerefovab

a Institute of Applied Mathematics and Automation, Nalchik
b North-Caucasus Federal University
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DOI: https://doi.org/10.36535/0233-6723-2023-221-63-70
Abstract: In this paper, we examine boundary-value problems for the inhomogeneous humidity transport equation with variable coefficients and the Caputo fractional derivative in time. Using the method of energy inequalities, we obtain a priori estimates for solutions of the first and third boundary-value problems, which imply the uniqueness and stability of solutions.
Keywords: boundary-value problem, Aller–Lykov equation, a priori estimate, fractional differential equation, regularized fractional derivative, Caputo derivative.
Document Type: Article
UDC: 517.95
MSC: 35Q99
Language: Russian
Citation: M. A. Kerefov, S.Kh. Gekkieva, B. M. Kerefov, “First boundary-value problem for the Aller–Lykov equation with the Caputo fractional derivative”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 221, VINITI, Moscow, 2023, 63–70
Citation in format AMSBIB
\Bibitem{KerGekKer23}
\by M.~A.~Kerefov, S.Kh.~Gekkieva, B.~M.~Kerefov
\paper First boundary-value problem for the Aller--Lykov equation with the Caputo fractional derivative
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 221
\pages 63--70
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1130}
\crossref{https://doi.org/10.36535/0233-6723-2023-221-63-70}
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