  Non-commutativity is a key feature of spacetime geometry. The current article
explores the traversable wormhole solutions in the framework of $f(R,L_m)$
gravity within non-commutative geometry. By using the Gaussian and Lorentzian
distributions, we construct tideless wormholes for the nonlinear $f(R,L_m)$
model $f(R,L_m)=\dfrac{R}{2}+L_m^\alpha$. For both cases, we derive shape
functions and discuss the required different properties with satisfying
behavior. For the required wormhole properties, we develop some new
constraints. The influence of the involved model parameter on energy conditions
is analyzed graphically which provides a discussion about the nature of exotic
matter. Further, we check the physical behavior regarding the stability of
wormhole solutions through the TOV equation. An interesting feature regarding
the stability of the obtained solutions via the speed of sound parameters
within the scope of average pressure is discussed. Finally, we conclude our
results.
