Time-fractional telegraph equation of distributed order in higher dimensions

Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, Milton

http://hdl.handle.net/10400.8/7512

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Authors

Vieira, Nelson

Rodrigues, M. Manuela

Ferreira, Milton

Abstract(s)

In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in Rn 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.

Keywords

Time-fractional telegraph equation Distributed order Laplace, Fourier and Mellin transforms Fox H-functions Fractional moments Tauberian theorems

URI

http://hdl.handle.net/10400.8/7512

Citation

N. Vieira, M.M. Rodrigues, and M. Ferreira, Time-fractional telegraph equation of distributed order in higher dimensions, Commun. Nonlinear Sci. Numer. Simul., Vol. 102, 2021, Page: 105925