Non-local boundary value problem for a system of equations with the partial derivatives of fractional order

We study a non-local boundary value problem in a rectangular domain for a linear system of equations with partial fractional Riemann–Liouville derivatives with constant coefficients. The eigenvalues of matrix coefficients in the main part have fixed sign, which is an essential feature of such systems. These systems can be divided into two types which differ in terms of formulation of the correct boundary value problems. The system under investigation relates to the type II, i.e. to systems with the eigenvalues of matrix coefficients in the main part having different signs. We prove the existence and uniqueness theorem for the solution of the investigated boundary value problem. The conditions for the unique solvability of the problem are obtained in terms of the eigenvectors of the matrix coefficients in the main part of the system.