One inverse source problem generated by the Dunkl operator

TL;DR

This paper studies time-fractional pseudo-parabolic equations generated by the Dunkl operator, establishing well-posedness, explicit solutions, and solving an inverse source problem with numerical validation.

Contribution

It introduces a new inverse source problem related to Dunkl operator-generated equations, providing existence, uniqueness, and stability results.

Findings

Well-posedness of the forward problem established

Explicit formulas for solutions derived

Existence and uniqueness of the inverse source solution proved

Abstract

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.