Direct and inverse problems for time-fractional heat equation generated by Dunkl operator
Bekbolat B. Serikbaev D. Tokmagambetov N.
1 June 2023De Gruyter Open Ltd
Journal of Inverse and Ill-Posed Problems
2023#31Issue 3393 - 408 pp.
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. 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.
Cauchy problem , direct problem , Dunkl operator , Dunkl transform , heat equation , inverse Dunkl transform , inverse problem
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
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