A solution to a boundary-value problem for integro-differential equations with weakly singular kernels

A linear boundary value problem for a system of integro-differential equations with weakly singular kernels is considered. Questions of the unique solvability and the construction of algorithms for finding solution of the considered problem are studied. Conditions for the solvability of the boundary value problem for a system of integro-differential equations with weakly singular kernels are established using the Dzhumabaev parametrization method based on splitting the interval and introducing additional parameters. Necessary and sufficient conditions for the solvability of the two-point problem for the integro-differential equations with weakly singular kernels are received.