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 modified Chaplygin gas as fluid source. Associated with scalar field model, we determined Hubble parameter a generating function in terms field. Instead hyperbolic function, taken Jacobi elliptic Abel obtained Chaplygin-Jacobi (MCJG) Chaplygin-Abel (MCAG) equation states, respectively. Next, assumed that filled dark matter, radiation, energy. The sources energy candidates are MCJG MCAG. constrained parameters by recent observational data analysis. Using $\chi^{2}$ minimum test (maximum likelihood estimation), best fit values OHD+CMB+BAO+SNIa joint To examine viability MCAG models, deviations information criteria like $\triangle$AIC, $\triangle$BIC $\triangle$DIC. evolutions cosmological cosmographical (like state, deceleration, jerk, snap, lerk, statefinder, Om diagnostic) been studied for our parameters. check classical stability examined square speed sound $v_{s}^{2}$ interval $(0,1)$ expansion universe.