<p>The theoretical, numerical, and experimental demonstration of optical fraction-al-order integration is presented using a Fabry-Pérot interferometer made up of two fiber Bragg gratings. A spectral filtering behavior consistent with fractional-order integration is demonstrated by modeling the interferometer using the transfer matrix method and de-riving analytical expressions. It is shown that, under appropriate design conditions, the output light pulse corresponds to the mathematical result of applying a fractional integration operator to the input light pulse. This behavior is confirmed through numerical simulations and validated experimentally by fabricating a customized Fabry-Pérot interferometer, in which two fiber Bragg gratings are recorded in a photosensitive optical fiber. Analytical expressions relating the integration order to the reflectivity of a fiber Bragg grating are also derived, together with an analysis of the bandwidths that this optical de-vice can process. To the best of our knowledge, this is the first experimental demonstration of all-fiber fractional-order integration. The transmission of the fiber interferometer is experimentally characterized. Its performance as a photonic fractional integrator is demonstrated using light pulses as input. The results indicate that fractional-order operators can be implemented in an all-optical manner using fiber-optic technology.</p>