The well-posedness of an \(hp\)-version time-stepping discontinuous Galerkin (DG) method for the numerical solution of fractional superdiffusion evolution problems is studied. The paper is organized as follows: Section 1 is an introduction. In Section 2, some technical assumptions and notations are fixed and the \(hp\)-version time-stepping DG method is introduced. In Section 3, main results regarding the well-posedness of the approximate solutions are proved. Section 4 is devoted to the error analysis of the methods and to the proof of convergence results. The series of numerical examples are presented in Section 5.