Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University644910.18287/2541-7525-2018-24-3-23-29UnknownBOUNDARY VALUE PROBLEM FOR THE ALLER — LYKOV MOISTURE TRANSPORT GENERALIZED EQUATION WITH CONCENTRATED HEAT CAPACITYKerefovM. A.morenov@ssau.ruNakhushevaF. M.morenov@ssau.ruGekkievaS. Kh.morenov@ssau.ruKabardino-Balkarian State University named after H.M. BerbekovKabardino-Balkarian Scientific Center of the Russian Academy of Sciences1111201824323291101201911012019Copyright © 2018, Kerefov M.A., Nakhusheva F.M., Gekkieva S.K.2018<p>The article considers the Aller Lykov equation with a Riemann Liouville fractional time derivative, boundary conditions of the third kind and with the concentrated specific heat capacity on the boundary of the domain. Similar conditions arise in the case with a material of a higher thermal conductivity when solving a temperature problem for restricted environment with a heater as a concentrated heat capacity. Analogous conditions also arise in practices for regulating the water-salt regime of soils, when desalination of the upper layer is achieved by draining of a surface of the flooded for a while area. Using energy inequality methods, we obtained an a priori estimate in terms of the Riemann Liouville fractional derivative, which revealed the uniqueness of the solution to the problem under consideration.</p>уравнение Аллера — Лыкова, дробная производная, нелокальная задача, обобщенное уравнение влагопереноса, сосредоточенная теплоемкость, метод энергетических неравенств, априорная оценка, краевая задача.Aller’s — Lykov equation, fractional derivative, nonlocal problem, moisture transfer generalized equation, concentrated heat capacity, inequalities method, a priori estimate, boundary value problem.[[1] Barenblat G.I., Zheltov Yu.P., Kochina I.N. Ob osnovnykh predstavleniiakh teorii fil’tratsii odnorodnykh zhidkostei v treshchinovatykh porodakh [About the main submissions of the theory of filtration of uniform liquids in jointed breeds]. 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