Analysis of direct and inverse problems for a fractional elastoplasticity model

Tatar, Salih; Ulusoy, Süleyman

doi:10.2298/fil1703699t

Cited by 10 publications

(7 citation statements)

References 29 publications

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“…The difference of our study from the studies in the references [31][32][33][34][35][36][37][38][39][40][41][42][43] is that the unknown of the inverse problem is non-linear, i.e., it depends on the solution u. This is a relatively new topic and there are only a few works, see [44][45][46]. In [44], the unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients.…”

Section: −β Tmentioning

confidence: 96%

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

et al. 2023

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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.

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Section: −β Tmentioning

confidence: 96%

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

et al. 2023

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“…The difference of the current study from the references [33]- [46] is that the unknown of the inverse problem is non-linear, i.e depends on the solution u. This is a relatively new topic and there are only few works, see [47]- [49]. In [47], the unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients.…”

Section: Introductionmentioning

confidence: 92%

“…This is a relatively new topic and there are only few works, see [47]- [49]. In [47], the unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients. The authors prove that the direct problem has a unique solution and show the continuous dependence of the solution of the corresponding direct problem on the unkown coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…Then, existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coefficients. In [48], the authors study the numerical solutions of the direct and the inverse problems in [47] and mention about an application of the governing equation in the materials sciences. An inverse problem for the nonlinear time-fractional diffusion equation (1.12) is studied in [49].…”

Section: Introductionmentioning

confidence: 99%

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

Zeki

Tinaztepe

Tatar

et al. 2022

Preprint

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Direct and inverse problems for a nonlinear time fractional equation are studied. It is proved that the direct problem has a unique weak solution and the solution depends continuously on the nonlinear coefficient. Then it is shown that the inverse problem has a quasi-solution. The direct problem is solved by method of lines using an operator approach. A quasi-Newton optimization method is used for the numerical solution to the inverse problem. Tikhonov regularization is used to overcome the ill-posedness of the inverse problem. Numerical examples with noise free and noisy data illustrate applicability and accuracy of the proposed method to some extent.

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“…Notice that fractional direct and inverse Cauchy type problems have been studied by many authors since their applications and the intrinsic development of the fractional calculus theory. We refer, for instance, the sources [10,18,28,29,30,37,38,39,41,42,47] and references therein. The following books [9,19,27,40,46] as well.…”

mentioning

confidence: 99%

Generalized fractional Dirac type operators

Restrepo,

Ruzhansky,

Suragan

2021

Preprint

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We introduce a class of fractional Dirac type operators with timevariable coefficients by means of a Witt basis and the Riemann-Liouville fractional derivative with respect to another function. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method [17] to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.

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Analysis of direct and inverse problems for a fractional elastoplasticity model

Cited by 10 publications

References 29 publications

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

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

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

Generalized fractional Dirac type operators

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