Generalization of Hallaire-Luikov Moisture Transfer Equation: Direct Problem with the $\psi$-Prabhakar Operator

This paper focuses on the analysis of an initial-boundary value (direct) problem for the Hallaire-Luikov moisture transfer equation involving the $\psi$-Prabhakar integral-differential operator of fractional order.

We establish the existence, uniqueness, and stability of the solution to the formulated problem.

To construct the solution, we employ the method of separation of variables and the method of successive approximations (iteration method), and obtain the solution to the considered problem in an explicit form.

Furthermore, the solution is expressed in terms of a novel quadrivariate Mittag-Leffler-type function.

An a priori estimate for the problem is also established.