An Inverse Problem for a Two-Dimensional Time-Fractional Sideways Heat Equation

Liu, Songshu; Feng, Lixin

doi:10.1155/2020/5865971

Cited by 7 publications

(4 citation statements)

References 39 publications

(41 reference statements)

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“…As a result, this subject draws interest of many scientists in various research areas [1,2,3,4,5,6,7,8,9,10,11,12]. Therefore, inverse problems including fractional differential equations becomes an essential part of diverse processes in science [13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Inverse coefficient problem by fractional Taylor series method

Mine Aylin,

Ali

2023

AUCMCS

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This study focus on determining the unknown function of time or space in space-time fractional differential equation by fractional Taylor series method. A significant advantage of this method is that over-measured data is not used unlike most inverse problems. This advantage allows us to determine the unknown function with less error. The presented examples illustrate that the obtained solutions are in a high agreement with the exact solutions of the corresponding inverse problems.

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Section: Introductionmentioning

confidence: 99%

Inverse coefficient problem by fractional Taylor series method

Mine Aylin,

Ali

2023

AUCMCS

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“…Compared to the 1D setting, the literature of fractional diffusion equation in 2D or higher dimensional setting is much more scarce. Some articles [25][26][27][28] study the following 2D homogeneous fractional diffusion equation:…”

Section: Introductionmentioning

confidence: 99%

Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation

2022

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The inverse and ill-posed problem of determining a solute concentration for the two-dimensional nonhomogeneous fractional diffusion equation is investigated. This model is much worse than its homogeneous counterpart as the source term appears. We propose a modified kernel regularization technique for the stable numerical reconstruction of the solution. The convergence estimates under both a priori and a posteriori parameter choice rules are proven.

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“…For the theoretical results of the stability and the uniqueness of the solution, a backward problem and inverse source problem for a multi-dimensional time-fractional diffusion equation were included in [28]. The authors of [29,30] managed the inverse problem for the two-dimensional time-fractional sideways heat equation in the infinite domain. Inverse problems for two-dimensional time-fractional diffusion equation were also considered in [29,[31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

2021

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The article presents a method for solving the inverse problem of a two-dimensional anomalous diffusion equation with a Riemann–Liouville fractional-order derivative. In the first part of the present study, the authors present a numerical solution of the direct problem. For this purpose, a differential scheme was developed based on the alternating direction implicit method. The presented method was accompanied by examples illustrating its accuracy. The second part of the study concerned the inverse problem of recreating the model parameters, including the orders of the fractional derivative, in the anomalous diffusion equation. Equations of this type can be used to describe, inter alia, the heat conductivity in porous materials. The ant colony optimization algorithm was used to solve this problem. The authors investigated the impact of the distribution of measurement points, the use of different mesh sizes, and the input data errors on the obtained results.

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An Inverse Problem for a Two-Dimensional Time-Fractional Sideways Heat Equation

Cited by 7 publications

References 39 publications

Inverse coefficient problem by fractional Taylor series method

Inverse coefficient problem by fractional Taylor series method

Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation

Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

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