  The Schr\"odinger equation is a fundamental equation in quantum mechanics,
providing a means of understanding the behavior of quantum systems under a
range of potential energies. In particular, over the past decade, theoretical
studies have focused on adapting the Dunkl derivative to quantum mechanical
problems. This approach merely seeks to generalize traditional quantum
mechanical techniques through the utilization of differential-difference
operators associated with finite reflection groups, thereby providing solutions
that are dependent on parity. In this manuscript, we investigate the analytical
solution of the time-dependent Schr\"odinger equation for a harmonic oscillator
with time-dependent mass and frequency, coupled with angular-dependent
potential energy by utilizing the Dunkl derivatives. To obtain the solution, we
employ the Lewis-Riesenfeld invariant methodology. Our approach broadens the
scope of quantum mechanical analyses, offering exact solutions and new insights
into dynamic quantum systems under varying conditions.
