Sharp time decay rates on a hyperbolic plate model under effects of an intermediate damping with a time-dependent coefficient

In this work we study decay rates for a hyperbolic plate equation under effects of an intermediate damping term represented by the action of a fractional Laplacian operator and a time-dependent coefficient. We obtain decay rates with very general conditions on the time-dependent coefficient (Theorem 2.1, Section 2), for the power fractional exponent of the Laplace operator (-Δ)θ, in the damping term, θ ∈ [0, 1]. For the special time-dependent coefficient b(t) = μ(1+t)α, α ∈ (0, 1], we get optimal decay rates (Theorem 3.1, Section 3).