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Title: Time-fractional telegraph equation of distributed order in higher dimensions
Author: Vieira, N.
Rodrigues, M. M.
Ferreira, M.
Keywords: Time-fractional telegraph equation
Distributed order
Laplace transform
Fourier transform
Mellin transform
Fox H-functions
Fractional moments
Tauberian Theorem
Issue Date: Nov-2021
Publisher: Elsevier
Abstract: In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in $\BR^n \times \BR^+$ is considered. By employing the technique of the Fourier, Laplace and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems, we study the asymptotic behaviour of the second-order moment (variance) in the time domain.
Peer review: yes
DOI: 10.1016/j.cnsns.2021.105925
ISSN: 1007-5704
Publisher Version:
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

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