known as radion) stabilization were extensively studied in [@GW; @GW_radion; @csaki; @julien; @ssg1; @ssg2; @tp1; @tp2; @tp3; @sumanta_cosmology; @anjan]. A generic feature of many of these models is that the bulk spacetime is endowed with high curvature scale $\sim$ 4 dimensional Planck scale.\
It is well known that Einstein-Hilbert action can be generalized by adding higher order curvature terms which naturally arise from diffeomorphism property of the action. Such terms also have their origin in String theory from quantum corrections. In this context $F(R)$ [@cruz; @nojirinew; @laurentis; @odintsovnew; @faraoni; @felice; @paliathanasis], Gauss-Bonnet (GB) [@nojiri2; @nojiri3; @cognola] or more generally Lanczos-Lovelock gravity are some of the candidates in higher curvature gravitational theory.\
In general the higher curvature terms are suppressed with respect to Einstein-Hilbert term by Planck scale. Hence in low curvature regime, their contributions are negligible. However higher curvature terms become extremely relevant at the regime of large curvature. Thus for bulk geometry where the curvature is of the order of Planck scale, the higher curvature terms should play a crucial role. Motivated by this idea, in the present work, we consider a generalized warped geometry model by replacing Einstein-Hilbert bulk gravity action with a higher curvature $F(R)$ gravitational theory 