Abstract We have investigated decay channels and predicted some form-factor-dependent observables (e.g. branching ratio, forward–backward asymmetry, and lepton polarization asymmetry) considering a new physics contribution from the non-universal model. We have found that there is an appreciable difference between the standard model and model predictions. Recently, the lepton flavor non-universality parameters and have been measured by the LHCb Collaboration and found to be different from their standard model predictions. These deviations provide a hint of flavor non-universality in the lepton sector and motivate our research to look for new physics beyond the standard model. The and anomalies may be due to new physics in either the electron or the muon sector, or both. In our work, we have shown that the experimental results for and could be achieved in a non-universal model considering the new physics couplings to the muon sector only.