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)
Pages (from-to)	441-462
Number of pages	22
Journal	Numerical Algorithms
Volume	99
Issue number	1
DOIs	https://doi.org/10.1007/s11075-024-01883-z
State	Published - May 2025

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

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

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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, Tikhonov-type regularization method, error estimates, ill-posed problems, stability estimates",

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.",

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

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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 - 2025/5

Y1 - 2025/5

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 - Tikhonov-type regularization method

KW - error estimates

KW - ill-posed problems

KW - stability estimates

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UR - https://www.scopus.com/pages/publications/105003305411#tab=citedBy

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VL - 99

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JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 1

ER -

A Tikhonov-type regularization method for Caputo fractional derivative

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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