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We have considered flat Friedmann-Robertson-Walker (FRW) model of theuniverse and reviewed the modified Chaplygin gas as the fluid source.Associated with the scalar field model, we have determined the Hubble parameteras a generating function in terms of the scalar field. Instead of hyperbolicfunction, we have taken Jacobi elliptic function and Abel function in thegenerating function and obtained modified Chaplygin-Jacobi gas (MCJG) andmodified Chaplygin-Abel gas (MCAG) equation of states, respectively. Next, wehave assumed that the universe filled in dark matter, radiation, and darkenergy. The sources of dark energy candidates are assumed as MCJG and MCAG. Wehave constrained the model parameters by recent observational data analysis.Using $\chi^{2}$ minimum test (maximum likelihood estimation), we havedetermined the best fit values of the model parameters by OHD+CMB+BAO+SNIajoint data analysis. To examine the viability of the MCJG and MCAG models, wehave determined the values of the deviations of information criteria like$\triangle$AIC, $\triangle$BIC and $\triangle$DIC. The evolutions ofcosmological and cosmographical parameters (like equation of state,deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studiedfor our best fit values of model parameters. To check the classical stabilityof the models, we have examined the values of square speed of sound $v_{s}^{2}$in the interval $(0,1)$ for expansion of the universe.

Roles of Modified Chaplygin-Jacobi and Chaplygin-Abel Gases in FRW Universe