We form optical systems by using only free space portions and cylindri
cal lenses, and consider these systems as anamorphic fractional Fourie
r transformers, We dynamically adjust the transform order, scale facto
r and field curvature of both orthogonal dimensions of anamorphic frac
tional Fourier transformation by just changing the focal lengths of cy
lindrical lenses used in the proposed setups. Here, we also consider t
wo approaches for implementing cylindrical lenses with dynamically adj
ustable focal lengths. There may also be some other methods to obtain
cylindrical lenses having adjustable focal lengths which can successfu
lly be used in these proposed setups.