\frac{1}{2}G_{MN}R - R_{MN} + \frac{\alpha}{2}G_{MN}R^2&-&2\alpha RR_{MN}\nonumber\\ 
 - 2\alpha G_{MN}\Box R + 2\alpha \nabla_{M}\nabla_{N}R&=&-\frac{1}{2}\Lambda G_{MN}
 \label{field2}\end{aligned}$$

It may be shown that the solution of $G_{MN}$ in eqn.(\[grav.sol1.F(R)\_final\]) satisfies the above field equation to the leading order of $\kappa v_h$. It may be recalled that the equivalence of the chosen $F(R)$ model was transformed to the potential of the scalar-tensor model in the leading order of $\kappa v_h$. Thus it guarantees the validity of the solution of spacetime metric (i.e. $G_{MN}$) in the original $F(R)$ theory.\
Using the metric solution given in eqn.(\[grav.sol1.F(R)\_final\]), one calculates the five dimensional Ricci scalar as follows: $$\begin{aligned}
 R(y)&=&-20k^2 - \frac{20}{\sqrt{3}}e^{[-\frac{\sqrt{3}}{2}\kappa cr_cy k^2]}k^2\kappa c 
 - 5e^{[-2\frac{\sqrt{3}}{2}\kappa cr_cy k^2]}k^2\kappa^2 c^2
 \label{ricci_scalar_F(R)}\end{aligned}$$ where $c$ is an integration constant. The presence of higher curvature gravity admits a general class of warped spacetime solution where the bulk curvature depends on the extra dimensional coordinate, which is in contrast to original RS situation where the bulk curvature is constant. Therefore, the present construction may lead to a new phenomenological scenario in the context of braneworld Physics which includes the effects of higher curvature terms present in the gravitational action. We now show how the higher curvature terms affect the localization of fermion 