higher curvature parameter $\alpha$ increases, the peak of both left and right massless chiral wave function shift towards the visible brane. Thus $\alpha>0$ indicates more localization in comparison to RS situation. It may be mentioned that the condition $\alpha>0$ is in agreement with various astrophysical constraints for $F(R)=R+\alpha R^2$ as well as braneworld stability requirement \[see [@tp1]\].\
Moreover, using the solution of $\zeta_{L,R}(y)$ (in eqn. (\[solution2\])), we obtain the effective coupling [@rizzo] between radion and zeroth order fermionic KK mode as follows: $$\begin{aligned}
   \lambda_L&=&\sqrt{\frac{k}{24M^3}} e^{A(\pi r_c)} \bigg(\frac{e^{(k+2m_5)\pi r_c}}{e^{(k+2m_5)\pi r_c} -1}\bigg)\nonumber\\
   &\bigg[&\exp{\bigg[\frac{p}{2k}e^{(2+\nu)kr_c\pi} - \frac{q}{4k}e^{-2(2+\nu)kr_c\pi}}\bigg]\bigg]^2
   \label{coupling 4}
  \end{aligned}$$ for left handed chiral mode and, $$\begin{aligned}
  \lambda_R&=&\sqrt{\frac{k}{24M^3}} e^{A(\pi r_c)} \bigg(\frac{e^{(k-2m_5)\pi r_c}}{e^{(k-2m_5)\pi r_c} -1}\bigg)\nonumber\\
   &\bigg[&\exp{\bigg[\frac{p}{2k}e^{(2+\nu)kr_c\pi} - \frac{q}{4k}e^{-2(2+\nu)kr_c\pi}}\bigg]\bigg]^2
   \label{coupling 5}
  \end{aligned}$$ for right handed mode.\
With the form of $p$ and $q$ given in eqn.(\[p\]) and eqn.(\[q\]), it is evident that the effective radion-fermion coupling increases (for both left and right chiral mode) with the higher curvature parameter $\alpha$. It is expected because the peak of both left and right chiral wave function get shifted towards the visible brane as $\alpha$ increases.\
To explore the radion phenomenology, we observe that the mass of radion field in the presence of higher order curvature term ($F(R)=R+\alpha R^2$) 