Nonlocal boundary-value problem for the generalized Аller–Lykov moisture transport equation

The mathematical modeling of different process types, for example, particle diffusion in a turbulent plasma, the propagation of heat in a thin rod, moisture transfer in soil, problems in mathematical biology and control problems, entails solving nonlocal boundary value problems. The paper considers a nonlocal boundary-value problem for the Aller–Lykov moisture transfer equation with a Riemann–Liouville time fractional derivative. The equation under consideration is a generalization of the Aller–Lykov equation obtained by introducing the concept of the fractal rate of humidity change, which explains the presence of flows moving against the water potential. For the solution to the problem, an a priori estimate has been obtained by the method of energy inequalities in terms of the fractional Riemann–Liouville derivative, which implies the uniqueness of the solution.