<p>This study investigates the influence of viscosity contributions from ion and dust particles on the dynamics of charge fluctuating dusty plasma. The analysis incorporates the motion of both positively charged ions and negatively charged, lighter dust particles, which are treated as mobile constituents alongside Maxwellian electrons. Utilizing the reductive perturbation technique, we derive the Korteweg–de Vries–Burgers (KdV–Burgers) equation, which serves as a framework for exploring the characteristics of dust and ion acoustic shock profiles. Our findings indicate that the viscosity within the dusty plasma plays a pivotal role in the dissipation processes, significantly impacting the propagation characteristics of dust and ion acoustic shocks. Furthermore, the study reveals that the nonlinear and dispersive coefficients are altered when accounting for the mobility of dust particles in conjunction with ions. As a result, both the amplitude and width of the dust and ion acoustic shock waves exhibit deviations from those observed in traditional dust-ion-acoustic waves, highlighting the complex interplay between particle dynamics and wave propagation in dusty plasma environments.</p>