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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 15, Issue 4

Issues

Fractional calculus for power functions and eigenvalues of the fractional Laplacian

Bartłlomiej Dyda
  • Faculty of Mathematics, University of Bielefeld, Postfach 10 01 31, D-33501, Bielefeld, Germany
  • Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland
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Published Online: 2012-09-29 | DOI: https://doi.org/10.2478/s13540-012-0038-8

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.

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

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

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About the article

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.

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© 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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