  In the present work, a new shape function is proposed inside a modified
$f(R)$ gravity and General Relativity in wormhole (WH) geometry. The shape
function obeyed all the desired conditions of WH geometry. The equation of
state (EoS) parameter, anisotropy parameter and the energy conditions are
computed. The tangential null energy conditions and the weak energy condition
are validated, as well as the radial energy conditions, which demonstrates the
nonappearance of exotic matter due to modified gravity allied with such a new
proposal.
