We discuss the problem of stabilization of wave equation by means of the standard or fractional derivative in boundary damping. The problem is being reduced to a selection between the proportional or fractional integrator of order 1 −
feedback controllers. The fractional integration leads to the strong asymptotic stability only, while the proportional feedback control can ensure the exponential stability. This means that exponential stability is not robust around the value
= 1. We shall discuss mathematical and control theory aspects of this fact.