Generalized Green's operator of the matrix integral-differential boundary value problem unsolved with respect to the derivative

Abstract

Solvability conditions and a structure of the generalized Green's operator of a linear Noether boundary value problem for a matrix integral-differential system unsolved with respect to the derivative, which generalizes integral-differential systems of the Fredholm type with a degenerate kernel. To solve the matrix integral-differential boundary value problem unsolved with respect to the derivative, original solvability conditions were used, as well as the structure of the general solution of the Sylvester-type matrix equation.