One inverse source problem generated by the Dunkl operator

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.