Direct and inverse problems for time-fractional heat equation generated by Dunkl operator-Reference-Cited by-同舟云学术

Direct and inverse problems for time-fractional heat equation generated by Dunkl operator

Published:2022-05-31 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Bekbolat Bayan¹,Serikbaev Daurenbek¹,Tokmagambetov Niyaz²^ORCID

Affiliation:

1. Institute of Mathematics and Mathematical Modeling , Almaty , Kazakhstan ; and Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium; and Al-Farabi Kazakh National University, Almaty, Kazakhstan

2. Department of Mathematics: Analysis, Logic and Discrete Mathematics , Ghent University , Ghent , Belgium ; and Institute of Mathematics and Mathematical Modeling Almaty, Kazakhstan

Abstract

Abstract In this paper, we study non–local in time evolution type equations generated by the Dunkl operator. Direct and inverse problems are investigated with the Caputo time-fractional heat equation with the parameter 0 < γ ≤ 1

{0<\gamma\leq 1}

. In particular, well-posedness properties are established for the forward problem. To adopt techniques of the harmonic analysis, we solve the problems in the Sobolev type spaces associated with the Dunkl operator. Our special interest is an inverse source problem for the Caputo–Dunkl heat equation. As additional data, the final time measurement is taken. Since our inverse source problem is ill-posed, we also show the stability result. Moreover, as an advantage of our calculus used here, we derive explicit formulas for the solutions of the direct and inverse problems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2021-0008/pdf

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