Determination of a Nonlinear Coefficient in a Time-Fractional Diffusion Equation

Autor:	Mustafa Zeki, Ramazan Tinaztepe, Salih Tatar, Suleyman Ulusoy, Rami Al-Hajj
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	fractional diffusion inverse problem quasi-solution existence and uniqueness method of lines Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 7, Iss 5, p 371 (2023)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract7050371
Popis:	In this paper, we study direct and inverse problems for a nonlinear time fractional diffusion equation. We prove that the direct problem has a unique weak solution and the solution depends continuously on the coefficient. Then we show that the inverse problem has a quasi-solution. The direct problem is solved by the method of lines using an operator approach. A quasi-Newton optimization method is used for the numerical solution to the inverse problem. The Tikhonov regularization is used to overcome the ill-posedness of the inverse problem. Numerical examples with noise-free and noisy data illustrate the applicability and accuracy of the proposed method to some extent.
Databáze:	Directory of Open Access Journals
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