Naimark Problem for an Ordinary Differential Equationwith a Fractional Discrete DistributedDifferentiation Operator

For an ordinary differential equation with a fractional discretely distributed differentiation operator, we study the Naimark problem in which the boundary conditions are specified in the form of linear functionals. This allows one to cover a fairly wide class of linear local and nonlocal conditions. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution to the problem under study is found in terms of special functions. The theorem of existence and uniqueness of the solution is proven.