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Flat spectrum radio quasar (FSRQ) is the most luminous blazar at the GeV
energies. In this paper, we probe the photon-axion-like particle (ALP)
oscillation effect on the latest very-high-energy (VHE) $\gamma$-ray
observations of the FSRQ 4C+21.35 (PKS 1222+216). The $\gamma$-ray spectra are
measured by the collaborations Major Atmospheric Gamma Imaging Cherenkov
Telescopes (MAGIC), Very Energetic Radiation Imaging Telescope Array System
(VERITAS), and Fermi Large Area Telescope (Fermi-LAT), which cover two activity
VHE flares of 4C+21.35 in 2010 and 2014. We show the spectral energy
distributions (SEDs) of these two phases under the null and ALP hypotheses, and
set the combined limit on the ALP parameter space. The 95% $\rm C.L.$ combined
limit set by the FSRQ 4C+21.35 observations measured by MAGIC, VERITAS, and
Fermi-LAT in the $m_a-g_{a\gamma}$ plane is roughly at the photon-ALP coupling
$g_{a\gamma} \gtrsim 8\times 10^{-12} \rm \, GeV^{-1}$ for the ALP mass
$[\,2\times 10^{-10}\, {\rm eV} \lesssim m_a \lesssim 2\times 10^{-8}\, \rm
eV\,]$. Compared with the constraint of NGC 1275 set by Fermi-LAT, no stringent
limit result is derived with the photon-ALP coupling $g_{a\gamma}$ from the
FSRQ 4C+21.35, while this result could slightly broaden the ALP mass $m_a$
limit at the low-mass region.
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