G-inflation: From the intermediate, logamediate and exponential models

The intermediate, logamediate and exponential inflationary models in the context of Galileon inflation or G-inflation are studied. By assuming a coupling of the form $G(\varphi ,X)\propto {\varphi }^{\nu }{X}^n$ in the action, we obtain different analytical solutions from the background cosmological perturbations assuming the slow-roll approximation. General conditions required for these models of G-inflation to be realizable are determined and discussed. In general, we analyze the condition of inflation and also we use recent astronomical and cosmological observations for constraining the parameters appearing in these G-inflationary models.