Abstract <p>In this paper, we study the existence and uniqueness of the solution of a mixed problem for a time-fractional space degenerate beam equation. We obtained the spectral problem for spatial variables by employing the method of separation of variables. We introduced an operator to demonstrate the existence of the eigenvalues and eigenfunctions of this spectral problem. We proved that this operator has a discrete spectrum. We seek the solution to the problem as a series in terms of these eigenfunctions. We established the existence and uniqueness of the solution for different values of the degeneration degree of the equation.</p>