  We introduce a new theoretical model to describe the emitting region in a
blazar jet. We assume a one-zone leptonic picture, and construct the particle
transport equation for a plasma blob experiencing low-energy, monoenergetic
particle injection, energy dependent particle escape, shock acceleration,
adiabatic expansion, stochastic acceleration, synchrotron radiation, and
external Compton radiation from the dust torus and broad line region. We
demonstrate that a one-zone leptonic model is able to explain the IR though
{\gamma}-ray spectrum for 3C 279 in 2008-2009. We determine that the broad-line
region seed photons cannot be adequately described by a single average
distribution, but rather we find that a stratified broad line region provides
an improvement in the estimation of the distance of the emitting region from
the black hole. We calculate that the jet is not always in equipartition
between the particles and magnetic field, and find that stochastic acceleration
provides more energy to the particles than does shock acceleration, where the
latter is also overshadowed by adiabatic losses. We further introduce a novel
technique to implement numerical boundary conditions and determine the global
normalization for the electron distribution, based on analysis of stiff
ordinary differential equations. Our astrophysical results are compared with
those obtained by previous authors.
