We propose and demonstrate an optically tunable photonic fractional temporal differentiator using a tilted fiber Bragg grating written in an erbium/ytterbium (Er-Yb) co-doped fiber. Thanks to the high absorption of the Er-Yb co-doped fiber, when it is pumped the refractive index is changed, and thus the phase of a cladding mode resonant wavelength is changed continuously by continuous tuning of the pumping power. By locating the wavelength of the input light wave at the location of a cladding mode resonant wavelength, a temporal differentiator with a tunable fractional order is achieved. The proposed technique is experimentally evaluated. A temporal differentiator with a tunable fractional order is demonstrated. The use of the fractional differentiator to implement temporal differentiation of a Gaussian pulse with a bandwidth of 28 and 75 GHz is also demonstrated.