Jeans instability of predictive model of baryonic and fermionic dark matter with the impact of dissipative force

•The study highlights how the introduction of dissipation influences the growth rate and damping effect observed in the system.•The condition of instability is unaffected by the dissipative effect.•The dissipation term shows a destabilizing effect on the growth rate. This study examines the Jeans instability and growth rate of a self-gravitating system made up of baryonic particles and dark matter with a source of dissipation. While treating dark matter using a quantum damped-hydrodynamic technique, we employed the classical hydrodynamic fluid approach for baryonic particles. We get the coupled system's dispersion relation by evaluating the equations. We examine the dispersion relation and the Jeans condition in various limiting circumstances and demonstrate how parameters influence growth rate with the use of graphical instances. We discovered that, irrespective of the jeans wave number, the dissipation source damps the growth rate. The study highlights how the introduction of dissipation influences the growth rate and damping effect observed in the system. Overall, the findings of this study provide valuable insights into the dynamics of self-gravitating systems and their evolution over time.