Naimark Problem for an Ordinary Differential Equation with a Fractional Discrete Distributed Differentiation Operator

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