  The particle acceleration of blazar jets is crucial to high-energy
astrophysics, yet the acceleration mechanism division in blazar subclasses and
the underlying nature of these mechanisms remain elusive. In this work, we
utilized the synchrotron spectral information (synchrotron peak frequency,
$\log \nu_{\rm sy}$, and corresponding curvature, $b_{\rm sy}$) of 2705 blazars
from the literature and studied the subject of particle acceleration in blazar
jets by analysing the correlation between $\log \nu_{\rm sy}$ and $1/b_{\rm
sy}$. Our results suggested that the entire sample follows an energy-dependent
probability acceleration (EDPA). Specifically, the low inverse Compton peak
sources (LCPs) follow the mechanism that fluctuations of fractional gain
acceleration (FFGA), while the high inverse Compton peak sources (HCPs) follow
an acceleration mechanism of EDPA. Our results indicated that the separation
between LCPs and HCPs results from the electron peak Lorentz factor
($\gamma_{\rm p}$), and the differentiation should originate from different
acceleration mechanisms. Moreover, our study revealed a transition in the
acceleration mechanism from FFGA to EDPA around $\log \nu_{\rm sy} \sim 15$
through a detailed analysis of binned-$\log \nu_{\rm sy}$. The mechanism of
FFGA dominates the particle acceleration in LCP jets because of stronger jets
and the EDPA dominates the particle energy gain in the HCPs due to a more
efficient acceleration process.
