A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations

Jingjun Zhao; Miaomiao Yang; Yang Xu

doi:10.1016/j.cam.2026.117881

A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations

Jingjun Zhao
, Miaomiao Yang
, Yang Xu^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

Abstract

Based on the properties of the time tempered Caputo-Hadamard fractional derivative, a family of modified Jacobi polynomials with explicit expressions is constructed. By combining the space-time discretization strategies with a variational formulation, a Petrov-Galerkin spectral method is developed for solving the tempered Caputo-Hadamard fractional diffusion equations, with the analysis including well-posedness, stability, and error estimates. Finally, some numerical experiments confirm the effectiveness of the proposed method.

Original language	English
Article number	117881
Journal	Journal of Computational and Applied Mathematics
Volume	489
DOIs	https://doi.org/10.1016/j.cam.2026.117881
State	Published - 1 Jan 2027
Externally published	Yes

Keywords

Error estimates
Modified Jacobi polynomial
Petrov-Galerkin spectral method
Stability
Tempered Caputo-Hadamard derivative

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10.1016/j.cam.2026.117881

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title = "A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations",

abstract = "Based on the properties of the time tempered Caputo-Hadamard fractional derivative, a family of modified Jacobi polynomials with explicit expressions is constructed. By combining the space-time discretization strategies with a variational formulation, a Petrov-Galerkin spectral method is developed for solving the tempered Caputo-Hadamard fractional diffusion equations, with the analysis including well-posedness, stability, and error estimates. Finally, some numerical experiments confirm the effectiveness of the proposed method.",

keywords = "Error estimates, Modified Jacobi polynomial, Petrov-Galerkin spectral method, Stability, Tempered Caputo-Hadamard derivative",

author = "Jingjun Zhao and Miaomiao Yang and Yang Xu",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier B.V.",

year = "2027",

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doi = "10.1016/j.cam.2026.117881",

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T1 - A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations

AU - Zhao, Jingjun

AU - Yang, Miaomiao

AU - Xu, Yang

PY - 2027/1/1

Y1 - 2027/1/1

N2 - Based on the properties of the time tempered Caputo-Hadamard fractional derivative, a family of modified Jacobi polynomials with explicit expressions is constructed. By combining the space-time discretization strategies with a variational formulation, a Petrov-Galerkin spectral method is developed for solving the tempered Caputo-Hadamard fractional diffusion equations, with the analysis including well-posedness, stability, and error estimates. Finally, some numerical experiments confirm the effectiveness of the proposed method.

AB - Based on the properties of the time tempered Caputo-Hadamard fractional derivative, a family of modified Jacobi polynomials with explicit expressions is constructed. By combining the space-time discretization strategies with a variational formulation, a Petrov-Galerkin spectral method is developed for solving the tempered Caputo-Hadamard fractional diffusion equations, with the analysis including well-posedness, stability, and error estimates. Finally, some numerical experiments confirm the effectiveness of the proposed method.

KW - Error estimates

KW - Modified Jacobi polynomial

KW - Petrov-Galerkin spectral method

KW - Stability

KW - Tempered Caputo-Hadamard derivative

UR - https://www.scopus.com/pages/publications/105041326510

U2 - 10.1016/j.cam.2026.117881

DO - 10.1016/j.cam.2026.117881

M3 - 文章

AN - SCOPUS:105041326510

SN - 0377-0427

VL - 489

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 117881

ER -

A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations

Abstract

Keywords

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