A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations

Nguyen Van Duc; Thi Phong Nguyen

doi:10.1016/j.amc.2025.129567

A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations

Nguyen Van Duc, Thi Phong Nguyen

Mathematical Sciences

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

Abstract

This paper investigates a Tikhonov-type approach for addressing inverse source problems related to time-space fractional parabolic equations. The method ensures a Hölder-type error estimate for the regularized solution at an optimal order, enabling a fixed parameter choice rule that does not depend on the data. Efficient numerical algorithms are devised for practical implementation, accompanied by numerical examples.

Original language	English (US)
Article number	129567
Journal	Applied Mathematics and Computation
Volume	507
DOIs	https://doi.org/10.1016/j.amc.2025.129567
State	Published - Dec 15 2025

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

Keywords

Conjugate gradient
Fractional derivative
Inverse source problem
Singular value decomposition
Tikhonov regularization
Time-space fractional parabolic equation

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10.1016/j.amc.2025.129567

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title = "A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations",

abstract = "This paper investigates a Tikhonov-type approach for addressing inverse source problems related to time-space fractional parabolic equations. The method ensures a H{\"o}lder-type error estimate for the regularized solution at an optimal order, enabling a fixed parameter choice rule that does not depend on the data. Efficient numerical algorithms are devised for practical implementation, accompanied by numerical examples.",

keywords = "Conjugate gradient, Fractional derivative, Inverse source problem, Singular value decomposition, Tikhonov regularization, Time-space fractional parabolic equation",

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AU - Nguyen, Thi Phong

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N2 - This paper investigates a Tikhonov-type approach for addressing inverse source problems related to time-space fractional parabolic equations. The method ensures a Hölder-type error estimate for the regularized solution at an optimal order, enabling a fixed parameter choice rule that does not depend on the data. Efficient numerical algorithms are devised for practical implementation, accompanied by numerical examples.

AB - This paper investigates a Tikhonov-type approach for addressing inverse source problems related to time-space fractional parabolic equations. The method ensures a Hölder-type error estimate for the regularized solution at an optimal order, enabling a fixed parameter choice rule that does not depend on the data. Efficient numerical algorithms are devised for practical implementation, accompanied by numerical examples.

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KW - Fractional derivative

KW - Inverse source problem

KW - Singular value decomposition

KW - Tikhonov regularization

KW - Time-space fractional parabolic equation

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JO - Applied Mathematics and Computation

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A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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