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A continuously tunable microwave fractional Hilbert transformer (FHT) implemented based on a photonic microwave delay-line filter is proposed and demonstrated. The photonic microwave delay-line filter with negative coefficients is realized based on polarization-modulation using a polarization modulator (PolM) and polarization-modulation to intensity-modulation conversion in an optical polarizer. The tunability of the fractional order is achieved by tuning the coefficient of the zeroth tap. An FHT with a tunable order from 0.3 to 1 is demonstrated. The accuracy of the FHT is evaluated; a phase deviation less than 5° within the passband is achieved.