Let M be an n-dimensional closed Riemannian manifold with metric g. Let
dμ=e^-φ(x)dν be the weighted measure and Δ_p,φ be the weighted p-Laplacian. In this article we will investigate monotonicity for the first eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Ricci-Bourguignon flow on closed Riemannian manifolds. We find the first variation formula for the eigenvalues of the weighted p-Laplacian on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and we obtain various monotonic quantities. At the end we find some applications in 2-dimensional and 3-dimensional manifolds and give an example.

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