A regularization method for time-fractional linear inverse diffusion problems

Nguyen Huy Tuan; Mokhtar Kirane; Vu Cam Hoan Luu; Bandar Bin-Mohsin

A regularization method for time-fractional linear inverse diffusion problems

Nguyen Huy Tuan, Mokhtar Kirane, Vu Cam Hoan Luu, Bandar Bin-Mohsin

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.

Original language	British English
Article number	290
Journal	Electronic Journal of Differential Equations
Volume	2016
State	Published - 26 Oct 2016

Keywords

Caputo fractional derivatives
Convergence estimate
Inverse advection-dispersion problem
Regularization method

Cite this

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title = "A regularization method for time-fractional linear inverse diffusion problems",

abstract = "In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.",

keywords = "Caputo fractional derivatives, Convergence estimate, Inverse advection-dispersion problem, Regularization method",

author = "Tuan, {Nguyen Huy} and Mokhtar Kirane and Luu, {Vu Cam Hoan} and Bandar Bin-Mohsin",

note = "Funding Information: Telecommunications Institute of Technology at Ho Chi Minh City, Vietnam. The second and fourth authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group no RG-1437-019. Publisher Copyright: {\textcopyright} 2016 Texas State University.",

year = "2016",

month = oct,

day = "26",

language = "British English",

volume = "2016",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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T1 - A regularization method for time-fractional linear inverse diffusion problems

AU - Tuan, Nguyen Huy

AU - Kirane, Mokhtar

AU - Luu, Vu Cam Hoan

AU - Bin-Mohsin, Bandar

N1 - Funding Information: Telecommunications Institute of Technology at Ho Chi Minh City, Vietnam. The second and fourth authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group no RG-1437-019. Publisher Copyright: © 2016 Texas State University.

PY - 2016/10/26

Y1 - 2016/10/26

N2 - In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.

AB - In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.

KW - Caputo fractional derivatives

KW - Convergence estimate

KW - Inverse advection-dispersion problem

KW - Regularization method

UR - http://www.scopus.com/inward/record.url?scp=84997228929&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84997228929

SN - 1072-6691

VL - 2016

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

M1 - 290

ER -

A regularization method for time-fractional linear inverse diffusion problems

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Keywords

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