On the question of the existence of a solution to the first boundary value problem for the Aller – Lykov moisture transfer equation with the operator of fractional discretely distributed differentiation

The paper investigates the first boundary value problem for the Aller – Lykov moisture transfer equation with the operator of fractional discretely distributed differentiation. Fractional derivatives included in the equation are understood in the Riemann – Liouville sense. The equation in question is a generalization of the classical Aller – Lykov equation. It takes into account the colloidal capillary-porous structure of the soil, including the presence of flows against the moisture potential. The existence of a solution to the first boundary value problem is proved by the Fourier method.