A Tikhonov-type regularization method for Caputo fractional derivative

Nguyen Van Duc; Thi Phong Nguyen; Nguyen Phuong Ha; Nguyen The Anh; Luu Duc Manh; Hoang Cong Gia Bao

doi:10.1007/s11075-024-01883-z

A Tikhonov-type regularization method for Caputo fractional derivative

Nguyen Van Duc, Thi Phong Nguyen, Nguyen Phuong Ha, Nguyen The Anh, Luu Duc Manh, Hoang Cong Gia Bao

Mathematical Sciences

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

Abstract

Stability estimates of Hölder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of Hölder type. Numerical results are presented to confirm the theory.

Original language	English (US)
Journal	Numerical Algorithms
DOIs	https://doi.org/10.1007/s11075-024-01883-z
State	Accepted/In press - 2024

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Caputo fractional derivative
error estimates
ill-posed problems
stability estimates
Tikhonov-type regularization method

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10.1007/s11075-024-01883-z

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title = "A Tikhonov-type regularization method for Caputo fractional derivative",

abstract = "Stability estimates of H{\"o}lder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of H{\"o}lder type. Numerical results are presented to confirm the theory.",

keywords = "Caputo fractional derivative, error estimates, ill-posed problems, stability estimates, Tikhonov-type regularization method",

author = "Duc, {Nguyen Van} and Nguyen, {Thi Phong} and Ha, {Nguyen Phuong} and Anh, {Nguyen The} and Manh, {Luu Duc} and Bao, {Hoang Cong Gia}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

year = "2024",

doi = "10.1007/s11075-024-01883-z",

language = "English (US)",

journal = "Numerical Algorithms",

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T1 - A Tikhonov-type regularization method for Caputo fractional derivative

AU - Duc, Nguyen Van

AU - Nguyen, Thi Phong

AU - Ha, Nguyen Phuong

AU - Anh, Nguyen The

AU - Manh, Luu Duc

AU - Bao, Hoang Cong Gia

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024

Y1 - 2024

N2 - Stability estimates of Hölder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of Hölder type. Numerical results are presented to confirm the theory.

AB - Stability estimates of Hölder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of Hölder type. Numerical results are presented to confirm the theory.

KW - Caputo fractional derivative

KW - error estimates

KW - ill-posed problems

KW - stability estimates

KW - Tikhonov-type regularization method

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UR - http://www.scopus.com/inward/citedby.url?scp=85200055549&partnerID=8YFLogxK

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DO - 10.1007/s11075-024-01883-z

M3 - Article

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SN - 1017-1398

JO - Numerical Algorithms

JF - Numerical Algorithms

ER -

A Tikhonov-type regularization method for Caputo fractional derivative

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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