On the Solvability of an Initial-Boundary Value Problem for a Fractional Heat Equation with Involution

The present work is devoted to the study of methods for solving the Dirichlet boundary value problem for a class of nonlocal second-order partial differential equations with involutive mappings of arguments. The concept of a nonlocal analogue of the Laplace equation is introduced, which generalizes the classical Laplace equation. The problems are solved by applying the theory of matrices and the method of separation of variables. Research of the substantiation of the well-posedness of these problems is carried out, as well as the proof of existence and uniqueness theorems for solutions of the corresponding boundary value problems. Authors proposed the method that allows, using the theory of matrices, to reduce the study of a boundary value problem to another problem for a parabolic equation without involution.