brane as $\alpha$ increases.This may explain the invisibility of massive KK mode fermions in the search for signature of warped extra dimensions in collider Physics.\
Moreover, it can also be shown (from eqn.(\[solution3\])) that as the order of KK mode increases from $n=1$, the localization of fermions becomes sharper near Planck brane.\
It may be mentioned that the bulk fermion mass term ($m_5$) also affects the localization of fermion field. Using the solution of $\zeta_{L,R}(y)$ presented in eqn. (\[solution2\]), it can be shown that for a fixed value of backreaction parameter, the left chiral mode of zeroth KK fermion has higher peak values on TeV brane as the bulk fermion mass increases where as the right chiral mode shows the reverse nature, which is in agreement with [@jm; @tp_fermion].\

Fermion localization in the corresponding scalar-tensor (ST) theory
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Till now we have described the fermion localization in the original $F(R)$ gravity model. To bring out the equivalence in the ST theory, we need to transform the original Dirac lagrangian (shown in eqn.(\[1\])) into scalar-tensor version of the model and a conformal transformation of $G_{MN}$ (as mentioned in eqn.(\[conformal\])) fulfills the purpose. With such conformal transformation, $L_{Dirac}$ takes the following form: 