In 2012, Samet, Vetro and Vetro introduced the notion of alpha-psi-contractive mappings. They established some fixed point results for the mappings on complete metric spaces. In this paper by using main idea of the work, we introduce the concept of alpha-psi -contractive mappings on intuitionistic metric spaces and give some fixed point results about the mappings on complete intuitionistic metric spaces. Also, we give an application of our results about the existence of solution of a nonlinear fractional differential equation via a two-point boundary value condition.
