Abstract:
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.
Keywords:system of ordinary differential equations, fractional derivative, nonlocal boundary value problem, Green's function.