Spectral Approach to Fractional Power of Operator and Its Matrix Approximation

This article is devoted to constructing the fractional powers of operators and their matrix approximations. A key feature of this study is the use of a spectral approach that remains applicable even when the base operator does not generate a semigroup. Our main results include the convergence rate of matrix approximation, derived from resolvent estimates, and a practical algorithm for constructing matrix approximations. The theory is supported by examples.

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Publication Details

Journal
Fractal and Fractional
Published
2026-02-12
DOI
https://doi.org/10.3390/fractalfract10020121
Primary Topic
Fractional Differential Equations Solutions
Type
article
Field-Weighted Citation Impact
0.00
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article

Spectral Approach to Fractional Power of Operator and Its Matrix Approximation

Vassili N. Kolokoltsov, Elina Shishkina
Fractal and Fractional
Fractional Differential Equations Solutions
article

Spectral Approach to Fractional Power of Operator and Its Matrix Approximation

Vassili N. Kolokoltsov, Elina Shishkina
article en

Abstract

This article is devoted to constructing the fractional powers of operators and their matrix approximations. A key feature of this study is the use of a spectral approach that remains applicable even when the base operator does not generate a semigroup. Our main results include the convergence rate of matrix approximation, derived from resolvent estimates, and a practical algorithm for constructing matrix approximations. The theory is supported by examples.

Fractal and FractionalVol. 10(2)
Chechen State University (RU), National Research University Higher School of Economics (RU), Belgorod National Research University (RU), Lomonosov Moscow State University (RU), Moscow Center For Continuous Mathematical Education (RU), Voronezh State University (RU)
Reduced inequalities
Openalex Percentile: Top 61%
Fractional Differential Equations Solutions
DOIOpen Access PDFOpenAlex
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Spectral Approach to Fractional Power of Operator and Its Matrix Approximation — Vassili N. Kolokoltsov, Elina Shishkina · Fractal and Fractional (2026) | TGRS Research Map | TGRS