A boundary problem for the time-fractional Hallaire-Luikov moisture transfer equation with Hilfer derivative

We aim to prove a unique solvability of a boundary-value problem with Dirichlet conditions for the Hallaire-Luikov moisture transfer equation involving generalized fractional derivative (Hilfer derivative) in time. The formal solution to the problem has been obtained in a series form using the method of spectral expansion. Imposing certain conditions on given functions and using certain properties of the multinomial Mittag-Leffler function, we prove a uniform convergence of corresponding infinite series. Moreover, a number of properties of the multinomial Mittag-Leffler function in some particular cases are also presented. Finally, an example solution is provided to illustrate the obtained results.