In the lights of current BICEP2 observations accompanied with the PLANCK satellite results , it has been observed that the simple single field chaotic inflationary models provide a good agreement with their spectral index n _ { s } and large tensor-to-scalar ratio r ( 0.15 < r < 0.26 ) .
To explore the other simple models , we consider the fractional-chaotic inflationary potentials of the form V _ { 0 } \phi ^ { a / b } where a and b are relatively prime .
We show that such kind of inflaton potentials can be realized elegantly in the supergravity framework with generalized shift symmetry and a nature bound a / b < 4 for consistency .
Especially , for the number of e-folding from 50 to 60 and some a / b from 2 to 3 , our predictions are nicely within at least 1 \sigma region in the ( r - n _ { s } ) plane .
We also present a systematic investigation of such chaotic inflationary models with fractional exponents to explore the possibilities for the enhancement in the magnitude of running of spectral index ( \alpha _ { n _ { s } } ) beyond the simplistic models .