  The aim of this paper is to study time-fractional pseudo-parabolic type
equations generated by the Dunkl operator. The forward problem is considered
and its well-posedness is established. In particular, a prior estimates are
obtained in the Sobolev type spaces and, explicit formulas for solutions of the
problems are derived. Here we also deal with the left-sided Caputo fractional
time derivative.
  As an application, we investigate an inverse source problem. Existence and
uniqueness of the solution is proved. Moreover, we show that a solution pair is
continuously depending on the initial and additional data, finalizing with a
numerical test.
