After the Large Area Telescope (LAT) onboard Fermi gamma-ray space telescope operating in orbit, a large amount of data has shown that the GeV spectrum displays a power-law or log-parabola form. However, the GeV spectrum of individual sources may be more complex, with suspected hardening. But the reliability of the spectral hardening remains to be tested. To solve this problem, we searched 36 blazars with suspected hardening in the 𝛾-ray spectrum from literature. And we investigated their 𝛾-ray GeV spectrum by using the latest pass 8 data of Fermi-LAT. Then we studied the GeV spectrum evolution in different flare states of 6 blazars in combination with their light curves. We found that the 𝛾-ray spectral hardening in most of the sources are not reliable. For example, the GeV 𝛾-ray spectral hardening of Mrk 501 and 3C 279 do not exist.A significant (∼ 4𝜎) hardening at ∼ 1 GeV is found in the 𝛾-ray spectrum of 1ES 0502+675 during a moderately flaring state (August 7, 2009 to June 3, 2010). The photon index below and above the break energy is 2.36 ± 0.31 and 1.33 ± 0.11, respectively, which is the first case of blazars with obvious 𝛾-ray spectral hardening.In the frame of a one-zone synchrotron self-Compton (SSC) model, the spectral hardening is interpreted as the transition between the synchrotron component and the SSC component. This could be the result of a slight increase of the break/maximum Lorentz factor of the electrons.We will continue to pay attention to the 𝛾-ray spectral hardening of blazars in the follow-up research, and combine with data from other telescopes for further study.
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