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.

 

KEYWORDS: Hallaire–Luikov moisture transfer equation, Hilfer derivative, Multinomial Mittag–Leffler function, Multi-term time-fractional differential equation, Fourier series