The fractional Fourier transform (FRT) is expressed by means of propagation and thin-lens phase delay operators, and a large number of optical systems associated with it are found. At the same time, the output of optical systems is found in terms of the FRT, and the simplicity of the approach is illustrated with two examples. Mathematical definitions for the P-order convolution and correlation are proposed as generalizations of the classical ones such that, when the P-order FRT is applied to them, theorems that generalize the classical convolution and correlation are verified.