Neumann problem for an ordinary differential equation of fractional order

A linear ordinary differential equation of fractional order with constant coefficients is considered in the paper. Such equation should be subsumed into the class of discretely distributed order, or multi-term differential equations. The fractional differentiation is given by the Caputo derivative. We solve The Nuemann problem for the equation under study, prove the existence and uniqueness of the solution, find an explicit representation for solution in terms of the Wright function, and construct the respective Green function. It is also proveв that the real part of the spectrum of the problem may consist at most of a finite number of eigenvalues.