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Title: Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
Author: Ferreira, Milton dos Santos
Vieira, Nelson Felipe Loureiro
Keywords: Fractional partial differential equations
Fractional Laplace and Dirac operators
Caputo derivative
Fundamental solution
Issue Date: 2016
Publisher: Springer
Abstract: In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.
ISBN: 978-3-319-42528-3
Publisher Version:
Appears in Collections:CIDMA - Capítulo de livro
CHAG - Capítulo de livro

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