Exponential decay for a neutral one-dimensional viscoelastic equation

In this work we consider a viscoelastic string subject to a delay of neutral type. The delay occurs in the second time derivative. Although delays are known by their destructive nature, here we prove an exponential decay result. We shall use the multiplier method and modify the classical energy by judicious choices of other functionals. This would lead to an appropriate differential inequality which allows us to conclude. It seems that this issue has never been discussed before in the literature.