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In this paper the notion of Ricci $\rho$-soliton as a generalization of Riccisoliton is defined. We are motivated by the Ricci-Bourguignon flow to definethis concept. We show that if a 3- dimensional almost Kenmotsu Einsteinmanifold $M$ be a $\rho$-soliton, then $M$ is a Kenmotsu manifold of constantsectional curvature $-1$ and the $\rho$-soliton is expanding, with $\lambda=2$.

Ricci $\rho$-solitons on 3-dimensional $\eta$-Einstein almost Kenmotsu mandifolds