  The jets of blazars are renowned for their multi-wavelength flares and rapid
extreme variability; however, there are still some important unanswered
questions about the physical processes responsible for these spectral and
temporal changes in emission properties. In this paper, we develop a
time-dependent particle evolution model for the time-varying emission spectrum
of blazars. In the model, we introduce time-dependent electric and magnetic
fields, which consistently include the variability of relevant physical
quantities in the transport equation. The evolution on the electron
distribution is numerically solved from a generalized transport equation that
contains the terms describing the electrostatic, first-order and second-order
\emph{Fermi} acceleration, escape of particles due to both advection and
spatial diffusion, as well as energy losses due to the synchrotron emission and
inverse-Compton scattering of both synchrotron and external ambient photon
fields. We find that the light curve profiles of blazars are consistent with
the particle spectral evolution resulting from time-dependent electric and
magnetic fields, rather than the effects of the acceleration or the cooling
processes. The proposed model is able to simultaneously account for the
variability of both the energy spectrum and the light curve profile of the BL
Lac object Mrk 421 with reasonable assumptions about the physical parameters.
The results strongly indicate that the magnetic field evolution in the
dissipated region of a blazar jet can account for the variabilities.
