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Title: Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
Author: Ferreira, Milton dos Santos
Vieira, Nelson Felipe Loureiro
Keywords: Fractional Laplace operator
Riemann-Liouville fractional derivatives
Mittag-Leffler function
Time fractional diffusion-wave operator
Time fractional parabolic Dirac operator
Fundamental solutions
Caputo fractional derivative
Fractional moments
Issue Date: 1-Mar-2017
Publisher: Elsevier
Abstract: In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order $\beta \in ]0,2].$ Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order $\gamma>0$ are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter.
Peer review: yes
DOI: 10.1016/j.jmaa.2016.08.052
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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