Green's function of a boundary value problem for a system of ordinary differential fractional order equations

The paper investigates a nonlocal boundary value problem for a linear system of fractional order ordinary differential equations with constant coefficients. The fractional derivative of order $\alpha\in (0,1]$ is understood in the Riemann — Liouville sense. The boundary conditions connect the traces of the fractional integral of the desired vector function at the ends of the segment $[0,l].$ Using the Green's function method, a representation of the solution is obtained, and a theorem on the unique solvability of the boundary value problem under study is proved.