This study aims to generate a model for the problem of beamforming in fractional Fourier domain, through which a general solution for obtaining weighted beamforming in fractional Fourier domain for different criteria might be delivered. In order to generate this model, a description of fractional delay concept is presented, through which the string vector in fractional Fourier domain is calculated and a model for beamforming in fractional Fourier domain is generated which is similar to that used for obtaining weighted beamforming in time domain for narrow-band signals. To complement our solution, a method for obtaining the optimal fractional domain as well as direction of arrival in optimal fractional Fourier domain.