+e aim of this article is to introduce a new definition for the Fourier transform. +is new definition will be considered as one of the generalizations of the usual (classical) Fourier transform. We employ the new Katugampola derivative to obtain some properties of the Katugampola Fourier transform and find the relation between the Katugampola Fourier transform and the usual Fourier transform. +e inversion formula and the convolution theorem for the Katugampola Fourier transform are considered.