  This article explores matter bounce non-singular cosmology in $f(R,L_m)$
gravity. We consider two non-linear $f(R,L_m)$ functional forms, specifically,
$f(R,L_m) = \frac{R}{2} + \lambda R^2 + \alpha L_m$ and $f(R,L_m) = \frac{R}{2}
+ L_m ^\beta + \gamma$ representing a minimal coupling case. We derive the
corresponding Friedmann-like equations for both the assumed models in the FLRW
background, and then we present the impact of the model parameters along with
the parameter of bouncing scale factor on the equation of state parameter,
pressure, and the energy density. In addition, we examine the dynamical
behavior of cosmographic parameters such as jerk, lerk, and snap parameters.
Further, we find that the violation of the null energy condition along with the
strong energy condition depicts the non-singular accelerating behavior,
corresponding to both assumed non-linear $f(R,L_m)$ functions. Lastly, we
present the behavior of the adiabatic speed of sound to examine the viability
of the considered cosmological bouncing scenario.
