We are studying the mechanism of the cosmic model in the presence of GGPDE and matter in LRS Bianchi type-I space-time by the utilization of new holographic DE in Saez-Ballester theory. Here we discuss all the data for three scenarios, first is supernovae type Ia union data, second is SN Ia data in combination with BAO and CMB observations and third is combination with OHD and JLA observations. From this, we get a model of our universe, where its transit state from deceleration to acceleration phase. Here we have observed that the results yielded by cosmological parameters like $rho$ (energy density), EoS (equation of state), squared speed of sound $(v_s^2)$, $(omega_D-omega_D^{})$ and $(r-s)$ plane is compatible with the recent observational data. The $(omega_D-omega_D^{})$ trajectories in both thawing and freezing regions and the correspondence of the quintessence field with GGPD dark energy are discussed. Some physical aspects of the GGPDE models are also highlighted.
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