A generalization of the canonical and non-canonical theory of inflation is introduced in which the kinetic energy term in action is written as non-local term. The inflationary universe within the framework of considering this non-locality will be studied. To investigate the effects of non locality on the inflationary parameters we consider two well known models of inflationary scenario includes of chaotic and exponential inflation proposals. For such scenarios some important parameters include slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio and so on for both mentioned models, chaotic and exponential inflationary scenarios, will be calculated. Also the Hamilton-Jacobi formalism, as an easiest way to study the effect of perturbation based on e-folding number N, to investigate inflationary attractors will be used. The free theoretical parameters of this model will be compared with observations by means of Planck 2013, WMAP9+eCMB+BAO+H0 data sets in addition to BICEP2 data surveying. It will be shown that our theoretical results are in acceptable range in comparison to observations. For instance the tensor-to-scalar ratio for exponential potential, by considering BICEP2 is in best agreement in comparison with chaotic inflation.
