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Abstract This analysis explores the new wormhole (WH) solution in the background of teleparallel gravity with minimal matter coupling. To complete this study, we consider the conformal symmetry with non-zero Killing vectors. The exact shape function is computed by considering the linear equation of state with the phantom regime. The energy conditions are investigated for the calculated shape function with the equation of state parameter. The presence of exotic matter is confirmed due to the violation of the null energy condition. The current study also explores the physical properties of the epicyclic frequencies with quasi-periodic oscillations. In the astrophysical, epicyclic frequencies are extensively employed to explore the self-gravitating system. It is concluded that a stable WH solution is acceptable for WH geometry.
Mustafa et al. (Tue,) studied this question.