Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives

<abstract><p>In this paper, we consider the time-fractional telegraph equation of distributed order in higher spatial dimensions, where time derivative is sense Hilfer, thus interpolating between Riemann-Liouville and Caputo fractional derivatives. By employing techniques Fourier, Laplace, Mellin transforms, obtain a representation solution Cauchy problem associated with terms convolutions involving functions that are Laplace integrals Fox H-functions. Fractional moments first fundamental computed for special case double-order it analyzed detail asymptotic behavior second-order moment, by application Tauberian Theorem. Finally, exhibit plots variance showing its short long times, different choices parameters along small dimensions.</p></abstract>