Generalized Ghost Pilgrim Dark Energy Fractal Cosmology with Observational Constraint

In this work, we explore dark energy models, mainly ghost, generalized ghost, and generalized ghost pilgrim dark energy models within the framework of fractal cosmology. To obtain solutions for the field equations, we employ a parameterization of the deceleration parameter as proposed by \textit{R.K. Tiwari}. By utilizing Markov Chain Monte Carlo (MCMC) analysis, we impose constraints on the free parameters of the derived solutions. The analysis is based on observational datasets, including 57 data points from the Observational Hubble Data ($OHD$) and, 1048 points from the $Pantheon$ Supernovae sample. This approach allows us to assess the viability of the dark energy models in describing the current cosmic expansion. According to the effective equation-of-state parameter, the model maintains itself in the quintessence era and ultimately switches into the Einstein-de Sitter model. Furthermore, we investigate the statefinder, jerk, snap, and lerk parameters. The energy conditions of each model satisfy the weak and null energy conditions but violate the strong energy condition. We find that the $Om(z)$ curves for the data samples exhibit a consistently negative slope throughout the entire range.