The current study explores the Sharma-Mittal holographic dark energy (SMHDE) by considering Bianchi- \(VI_0\) space-time in Saez-Ballester’s theory. The model’s exact solutions are procured by assuming the relationship between metric potentials. The Hubble horizon is regarded as the Infrared cutoff to examine our model’s cosmic effects. The physical behavior of the model is investigated by considering two fluids- SMHDE and pressureless matter. The behavior of the cosmological parameters, such as the deceleration parameter, EoS parameter, \(\rho _{de}\) , \(\rho _m\) , statefinder, and \(v_s^2\) , was evaluated with the help of their plots with respect to redshift(z) to study the nature of the universe. The figure of the deceleration parameter predicts that the present model transits from the deceleration to the acceleration period of the universe. The EoS parameter for this model agrees with the recent astrophysical observations, which lie within the range of quintessence region. In the case of statefinder and \(v_s^2\) , the model shows Chaplygin gas and stability throughout the region. The perturbation technique is used to evaluate the stability of the resulting model. Finally, the results of the current model support the existence of an accelerating universe with the present observational data.
