## Abstract

We calculate the fractional Laplacian Δα/2 for functions of the form u(x) = (1 − |x|2)+p and v(x) = x d u(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

Show Summary Details# Fractional calculus for power functions and eigenvalues of the fractional Laplacian

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Editor-in-Chief: Kiryakova, Virginia

IMPACT FACTOR 2018: 3.514

5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891

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- Online
- ISSN
- 1314-2224

Bartłlomiej Dyda

We calculate the fractional Laplacian Δα/2 for functions of the form u(x) = (1 − |x|2)+p and v(x) = x d u(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

MSC: Primary 35P15; Secondary 60G52, 31C25

Keywords: fractional Laplacian; ball; killed stable process; eigenvalue; power function; hypergeometric function

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**Published Online**: 2012-09-29

**Published in Print**: 2012-12-01

**Citation Information: **Fractional Calculus and Applied Analysis, Volume 15, Issue 4, Pages 536–555, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-012-0038-8.

© 2012 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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