Compared with symmetrical optical system,the optical system which consists of non-spherical lens can implement some special mathematical transforms. Based on the paraxial approximation,the tapered lens are investigated by geometrical optics,and the transmission function is derived. Furthermore,the transmission functions of cone and cylinder lens are also derived. With the help of these conclusions,the optical system consisting of double cylinder lens is constructed. This setup is the basic unit to implement anamorphic fractional Fourier transform. Finally,on the basis of scalar diffraction theory,the analytical solution is obtained. Furthermore,the system parameters are studied in detail in order to satisfy the requirements for various fractional Fourier transforms.