One inverse source problem generated by the Dunkl operator
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- arXiv:
- arXiv:2308.01232
- Bibcode:
- 2023arXiv230801232B
- Keywords:
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- Mathematics - Analysis of PDEs;
- Primary 35R30;
- Secondary 35R11;
- 35C15
- E-Print:
- 20 pages, 2 figures