  Primordial black holes (PBHs) can be significant sources of axions and
axion-like particles (ALPs) in the Universe as the Hawking radiation of the PBH
includes light particles when the Hawking temperature exceeds the particle's
mass. Once produced, as axions predominantly decay into photons, we may detect
the enhanced photon spectrum using sensitive detectors. We introduce a new
methodology by defining the time-varying decay process for particles to fly and
decay over time on a cosmological scale. This paper provides the estimated
photon spectrum and the flux under some simplified assumptions about PBH, 1)
monochromatic mass spectrum and 2) isotropic distribution at cosmological
scales. Future detectors, such as e-ASTROGAM, have great chances of detecting
the signal.
