  The X-ray spectral curvature of blazars is traditionally explained by an
empirical log-parabola function characterized by three parameters, namely the
flux, curvature and spectral index at a given energy. Since their exact
relationship with the underlying physical quantities is unclear, interpreting
the physical scenario of the source through these parameters is difficult. To
attain an insight on the X-ray spectral shape, we perform a detailed study of
the X-ray spectra of the blazar MKN 421, using an analytical model where the
electron diffusion from the particle acceleration site is energy-dependent. The
resultant synchrotron spectrum is again determined by three parameters, namely,
the energy index of the escape time scale, the quantity connecting the electron
energy to the observed photon energy and the normalization. The X-ray
observations of MKN 421, during July 2012 - April 2013 by NuSTAR and Swift-XRT
are investigated using this model and we find a significant correlation between
model parameters and the observational quantities. Additionally, a strong
anti-correlation is found between the fit parameters defining the spectral
shape, which was not evident from earlier studies using empirical models. This
indicates the flux variations in MKN 421 and possibly other blazars, may arise
from a definite physical process that needs to be further investigated.
