Geodesic
First boundary-value problem for the Aller--Lykov equation with the Caputo fractional derivative
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 221 (2023), pp. 63-70

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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, a priori estimate, fractional differential equation, regularized fractional derivative, Caputo derivative.
Mots-clés : Aller–Lykov equation 
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     title = {First boundary-value problem for the {Aller--Lykov} equation with the {Caputo} fractional derivative},
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M. A. Kerefov; S.Kh. Gekkieva; B. M. Kerefov. First boundary-value problem for the Aller--Lykov equation with the Caputo fractional derivative. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 221 (2023), pp. 63-70. http://geodesic.mathdoc.fr/item/INTO_2023_221_a6/