Traversable wormholes in $f(R)$ gravity with constant and variable redshift functions

The present paper is aimed at the study of traversable wormholes in $f(R)$ gravity with a viable $f(R)$ function defined as $f(R)=R-mu R_cBig(frac{R}{R_c}Big)^p$, where $R$ is scalar curvature, $mu$, $R_c$ and $p$ are constants with $mu, R_c>0$ and $0<p<1$ citep{Amendola}. The metric of wormhole is dependent on shape function $b(r)$ and redshift function $phi(r)$ which characterize its properties, so the shape function and redshift function play an important role in wormhole modeling. In this work, the wormhole solutions are determined for (i) $phi(r)=frac{1}{r}$ and (ii) $phi(r)=c$ (constant) with $b(r)=frac{r}{exp(r-r_0)}$ citep{godani1}. Further, the regions respecting the energy conditions are investigated.