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Title: Fundamental solution of the multi-dimensional time fractional telegraph equation
Author: Ferreira, Milton dos Santos
Rodrigues, Maria Manuela Fernandes
Vieira, Nelson Felipe Loureiro
Keywords: Time-fractional telegraph operator
Double Mellin-Barnes type integrals
Fundamental solutions
Caputo fractional derivative
Multivariate Mittag-Leffler functions
H-function of two variables
Issue Date: 1-Jul-2017
Publisher: de Gruyter
Abstract: In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation with time-fractional derivatives of orders $\alpha \in ]0,1]$ and $\beta \in ]1,2]$ in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS expressed in terms of a multivariate Mittag-Leffler function in the Fourier domain. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension $n$ and of the fractional parameters $\alpha$ and $\beta$.
Peer review: yes
DOI: 10.1515/fca-2017-0046
ISSN: 1314-2224
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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