The standard Fourier transform operator <i>F</i> is a particular case of the fractional order Fourier transform operator <i>F</i>^&alpha; (it is obtained for &alpha; = 1). In the same way that has been done for <i>F</i>, a sampling theorem for <i>F</i>^&alpha; is proposed for signals whose fractional Fourier transforms of order &alpha; have finite supports. An interpolation formula for fractional bandlimited functions is also deduced.