The fractional Langevin equation has been used to describe the evolution of the location of a stochastically growing interface in both planar and radial geometries. The interface dynamics can be driven by both local and non-local effects since the fractional derivative is non-local in terms of h unless ζ is an even, nonnegative integer. In this paper, we consider a general two-term Langevin equation and calculate the interface location in planar and radial geometries. We study the dynamics of the system for the stabilizing and destabilizing cases, and for different time limits. The analytical results are confirmed by numerically solving the fractional stochastic equations.