Stabilized Solution for a Time-Fractional Inverse Problem with an Unknown Nonlinear Condition

Babaei, Afshin; Banihashemi, Seddigheh

doi:10.1007/s10598-019-09460-z

Cited by 1 publication

(1 citation statement)

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“…Whereas, if not all characteristics (source term, coefficients or order of the PDE itself, initial or boundary conditions) of the problem are completely known, then we deal with an inverse problem. Depending on the missing information about the characteristics of the problem, we have different types of inverse problems , such an inverse-coefficient [1], [2], inverse problems of determining of order of differential equations [3], inverse source problems [4], inverse problems for determining the unknown boundary condition [5] and inverse initial problem [6]. The missing information will be determined using additional data.…”

Section: Introductionmentioning

confidence: 99%

Inverse source problems for degenerate time-fractional PDE

Al-Salti,

Karimov

2019

Preprint

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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.

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