Wormhole solutions in Rastall-like-torsion-trace gravity

In this paper, we explore the existence of traversable wormholes (WHs) inspired by the non-commutative (NC) geometry under conformal symmetries in the framework of Rastall-like-teleparallel gravity. Using "Gaussian" and "Lorentzian" energy distributions, we calculate the analytic solutions of the corresponding field equations in terms of some special math functions. For both distributions, we check the viability of energy conditions at the WH throat and interpret the results graphically for appropriate choices of free model parameters along with different choices of additional Rastall parameter lambda. We explain the possible constraints for the positivity of active gravitational mass, and check the stability of derived WH solutions. Moreover, the embedding diagrams for the shape functions are also plotted. Finally, it is concluded that the constructed WH solutions (sensitive for parameter lambda) are physically viable as well as stable in the presence of standard matter for Gaussian energy distribution and exotic matter for Lorentzian energy distribution.