  In this work, we obtain a new warped solution for a 5-dimensional $f(R) $
gravity in an anti de-Sitter bulk. The higher curvature term in the gravity
action is shown to modify the usual warped metric. The novel feature of this
modification leads to a natural geometric stabilization of the modulus/radion
field in the underlying effective theory on the visible 3-brane without the
need for any external stabilizing field. It is further shown that the
stabilized value of the modulus resolves the well-known gauge hierarchy problem
without any unnatural fine-tuning of the model parameters. This new solution
also opens up the possibilities of new signatures in various scenarios
formulated in the backdrop of higher dimensional space-time.
