  In this manuscript, we explore the existence of wormhole solutions exhibiting
spherical symmetry in a modified gravity namely $f(R,T)$ theory by involving
some aspects of non-commutative geometry. For this purpose, we consider the
anisotropic matter contents along with the well-known Gaussian and Lorentizian
distributions of string theory. For the sake of simplicity in analytic
discussions, we take a specific form of $f(R,T)$ function given by
$f(R,T)=R+\lambda T$. For both these non-commutative distributions, we get
exact solutions in terms of exponential and hypergeometric functions. By taking
some suitable choice of free parameters, we investigate different interesting
aspects of these wormhole solutions graphically. We also explored the stability
of these wormhole models using equilibrium condition. It can be concluded that
the obtained solutions are stable and physically viable satisfying the wormhole
existence criteria. Lastly, we discuss the constraints for positivity of the
active gravitational mass for both these distributions.
