Boundary value problem for the Aller–Lykov moisture transport generalized equation with concentrated heat capacity

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.