A continuously tunable microwave fractional Hilbert transformer (FHT) implemented based on a nonuniformly spaced photonic microwave delay-line filter is proposed and demonstrated. An FHT has a frequency response with a unity magnitude response and a phase response having a phase shift between 0 and π at the center frequency. A seven-tap photonic microwave delay-line filter with nonuniformly spaced taps is designed to provide such a frequency response. The advantage of using nonuniform spacing is that an equivalent negative coefficient can be achieved by introducing an additional time delay leading to a π phase shift, corresponding to a negative coefficient. An FHT operating at a center frequency around 8.165 GHz with a tunable order between 0.24 and 1 is implemented. A classical HT operating at a center frequency of 7.573 GHz with a bandwidth greater than 4.5 GHz is also implemented. The use of the classical HT to perform temporal Hilbert transform of a Gaussian-like electrical pulse is demonstrated.