Sampling plays a vital role in digital signal processing, as the continuous-time signal should be sampled and then rebuilt from its samples, this approach complies with the traditional sampling theorem. The sampling theorem for the conventional Fourier Transform should be generalized to the continuous fractional Fourier transform case since the continuous fractional Fourier transform (FRFT) has developed into a highly effective tool in signal processing, optics, and other Engineering and scientific applications. The continuous fractional Fourier transform of a specific rotation angle is proposed in this publication, along with a method for sampling continuous band-limited signals to derive their discrete-time versions without aliasing. The method is developed from the sampling theorem for the conventional Fourier transform and the integral formulation of the continuous fractional Fourier transform. The lemmas and corollary put forward in this work are generalizations of the Fourier transform's traditional form. Finally, the numerical outcomes convincingly support our study.