  The object of the present paper is to characterize two classes of almost
Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a
$(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or
gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product
$\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential
vector field is pointwise collinear with the Reeb vector field. Also, a
$(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with
the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic
space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property
$Q \cdot R = 0$ is proved.
