Inverse source problems for degenerate time-fractional PDE
Abstract
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one involves a time-degenerate partial differential equation. Solutions to both problem are expressed in series expansions. For the first problem, we obtained solutions in the form of Fourier-Legendre series. Convergence and uniqueness of solutions have been discussed. Solutions to the second problem are expressed in the form of Fourier-Sine series and they involve a generalized Mittag- Leffler type function. Moreover, we have established a new estimate for this generalized Mittag-Leffler type function. The obtained results are illustrated by providing example solutions using certain given data at the initial and final time.
Cite
@article{arxiv.1905.00362,
title = {Inverse source problems for degenerate time-fractional PDE},
author = {Nasser Al-Salti and Erkinjon Karimov},
journal= {arXiv preprint arXiv:1905.00362},
year = {2022}
}
Comments
12 pages, 8 figures