New general decay results in an infinite memory viscoelastic problem with nonlinear damping

This work is concerned with a viscoelastic equation with a nonlinear frictional damping and a relaxation function satisfying g(t) ≤ -ξ (t) gᵖ(t), t ≥ 0, 1≤ p<3/2 . We establish general decay rate results using the multiplier method and some properties of non-homogeneous ordinary differential inequalities. These results extend and improve many results in the literature.