Two different shape functions for wormholes in f (R) theory with non-commutative geometry and Lorentzian distribution

In this work, the solutions of traversable wormholes are investigated inside modified f (R) gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions b(r) = r(0)(a(r)/a(r)0), 0 < a < 1, and b(r) = r(0)(cosh(r(0))/cosh(r))(mu), 0 < mu < 1, are considered. The first shape function was proposed by Mishra and Sharma [A new shape function for wormholes in f(R) gravity and General Relativity, preprint (2020), arXiv: 2003.00298v1 [physics.gen-ph]], however the second is newly defined in this paper. The behaviors of both shape functions are analyzed with the throat radius r = r(0) = 1. The equation-of-state (EoS) parameter energy conditions, and anisotropy parameter are discussed with graphical point of view.