Roles of Modified Chaplygin-Jacobi and Chaplygin-Abel Gases in FRW
  Universe
  We have considered flat Friedmann-Robertson-Walker (FRW) model of the
universe and reviewed the modified Chaplygin gas as the fluid source.
Associated with the scalar field model, we have determined the Hubble parameter
as a generating function in terms of the scalar field. Instead of hyperbolic
function, we have taken Jacobi elliptic function and Abel function in the
generating function and obtained modified Chaplygin-Jacobi gas (MCJG) and
modified Chaplygin-Abel gas (MCAG) equation of states, respectively. Next, we
have assumed that the universe filled in dark matter, radiation, and dark
energy. The sources of dark energy candidates are assumed as MCJG and MCAG. We
have constrained the model parameters by recent observational data analysis.
Using $\chi^{2}$ minimum test (maximum likelihood estimation), we have
determined the best fit values of the model parameters by OHD+CMB+BAO+SNIa
joint data analysis. To examine the viability of the MCJG and MCAG models, we
have determined the values of the deviations of information criteria like
$\triangle$AIC, $\triangle$BIC and $\triangle$DIC. The evolutions of
cosmological and cosmographical parameters (like equation of state,
deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studied
for our best fit values of model parameters. To check the classical stability
of 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.
