  In this work, we introduce both gluon and quark degrees of freedom for
describing the partonic cascades inside the medium. We present numerical
solutions for the set of coupled evolution equations with splitting kernels
calculated for the static, exponential and Bjorken expanding media to arrive at
medium-modified parton spectra for quark and gluon initiated jets respectively.
We discuss novel scaling features of the partonic spectra between different
types of media. Next, we study the inclusive jet $R_{AA}$ by including
phenomenologically driven combinations of quark and gluon fractions inside a
jet. In addition, we have also studied the effect of the nPDF as well as vacuum
like emissions on the jet $R_{AA}$. Differences among the estimated values of
quenching parameter for different types of medium expansions are noted. Next,
the impact of the expansion of the medium on the rapidity dependence of the jet
$R_{AA}$ as well as jet $v_2$ are studied in detail. Finally, we present
qualitative results comparing the sensitivity of the time for the onset of the
quenching for the Bjorken profile on these observables. All the quantities
calculated are compared with the recent ATLAS data.
