Spectral Approximation to Fractional Integral Operators

Fuente: arXiv
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Main Authors: Liu, Xiaolin, Xu, Kuan
Format: Preprint
Published: 2025
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author Liu, Xiaolin
Xu, Kuan
author_facet Liu, Xiaolin
Xu, Kuan
contents We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional integrals of mapped Chebyshev polynomials and significantly outperforms existing methods. Through numerical examples, we highlight the broad applicability of these matrix approximations, including the solution of boundary value problems for fractional integral and differential equations. Additional applications include fractional differential equation initial value problems and fractional eigenvalue problems.
format Preprint
id arxiv_https___arxiv_org_abs_2506_19332
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Spectral Approximation to Fractional Integral Operators
Liu, Xiaolin
Xu, Kuan
Numerical Analysis
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional integrals of mapped Chebyshev polynomials and significantly outperforms existing methods. Through numerical examples, we highlight the broad applicability of these matrix approximations, including the solution of boundary value problems for fractional integral and differential equations. Additional applications include fractional differential equation initial value problems and fractional eigenvalue problems.
title Spectral Approximation to Fractional Integral Operators
topic Numerical Analysis
url https://arxiv.org/abs/2506.19332