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Title: Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives
Author: Vieira, N.
Rodrigues, M. M.
Ferreira, M.
Keywords: Time-fractional telegraph equation
Distributed order
Hilfer fractional derivative
Integral transforms
Fox H-function
Fractional moments
Tauberian Theorem
Issue Date: 29-Jul-2022
Publisher: AIMS Press
Abstract: In this paper, we consider the time-fractional telegraph equation of distributed order in higher spatial dimensions, where the time derivative is in the sense of Hilfer, thus interpolating between the Riemann-Liouville and the Caputo fractional derivatives. By employing the techniques of the Fourier, Laplace, and Mellin transforms, we obtain a representation of the solution of the Cauchy problem associated with the equation in terms of convolutions involving functions that are Laplace integrals of Fox H-functions. Fractional moments of the first fundamental solution are computed and for the special case of double-order distributed it is analyzed in detail the asymptotic behavior of the second-order moment, by application of the Tauberian Theorem. Finally, we exhibit plots of the variance showing its behavior for short and long times, and for different choices of the parameters along small dimensions.
Peer review: yes
DOI: 10.3934/era.2022184
ISSN: 2688-1594
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Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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