"Inverse Source Problems for Degenerate Time-Fractional PDE" by Nasser Al-Salti and Erkinjon Karimov

Progress in Fractional Differentiation & Applications

Article Title

Inverse Source Problems for Degenerate Time-Fractional PDE

Authors

Nasser Al-Salti, Department of Applied Mathematics and Science, National University of Science and Technology, Muscat, Oman\\ Frac. Diff. Research Group (DR/RG/03), Sultan Qaboos University, Muscat, OmanFollow
Erkinjon Karimov, Frac. Diff. Research Group (DR/RG/03), Sultan Qaboos University, Muscat, Oman\\ V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent-100170, UzbekistanFollow

Author Country (or Countries)

Oman

Abstract

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equations 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 problems 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 times.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080102

Recommended Citation

Al-Salti, Nasser and Karimov, Erkinjon (2022) "Inverse Source Problems for Degenerate Time-Fractional PDE," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 1, Article 2.
DOI: http://dx.doi.org/10.18576/pfda/080102
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss1/2

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