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Inverse Source Problems for Degenerate Time-Fractional PDE |
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PP: 39-52 |
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doi:10.18576/pfda/080102
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Author(s) |
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Nasser Al-Salti,
Erkinjon Karimov,
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Abstract |
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| 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.
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