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Title: First and second fundamental solutions of the time-fractional telegraph equation of order 2α
Author: Ferreira, Milton dos Santos
Rodrigues, Maria Manuela Fernandes
Vieira, Nelson Felipe
Keywords: Time-fractional telegraph equation
Telegraph Dirac operator
First and second fundamental solutions
Caputo fractional derivative
Multivariate Mittag-Leffler function
H-function of two variables
Issue Date: 2018
Publisher: AIP Publishing
Abstract: In this work we obtain the first and second fundamental solutions of the multidimensional time-fractional equation of order $2\alpha$, $\alpha \in ]0,1]$, where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time.
Peer review: yes
DOI: 10.1063/1.5081599
ISSN: 978-0-7354-1772-4
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Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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