  In this paper We have investigated a homogeneous and isotropic FRW
cosmological model with perfect fluid in the framework of $f(R,Lm)$ gravity. We
have explored for the non linear case of $f(R,L_m)$ model, namely $f(R,L_m) =
R/2 + L_m$ and obtained the solution by using the condition that the
deceleration parameter is a linear function of the Hubble parameter. We employ
57 Hubble data points and 1048 Pantheon supernovae type Ia data samples to
restrict the model parameters. Additionally, we employ Markoc Chain Monte Carlo
(MCMC) simulation for our statistical analysis. Additionally, we analyse the
jerk and om diagnostic parameters for our model using the parameter values that
were obtained.
