Fractional telegraph equations.
type: Item
instance of: scholarly article
title: Fractional telegraph equations.
zbMATH Open document ID: 1038.35142
DOI: 10.1016/S0022-247X(02)00394-3
author: Radu C. Cascaval
author: Eugene C. Eckstein
author: C. L. Frota
author: Jerome A. Goldstein
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The main result of this paper is the following. Let \(A=A^{*}\) be a positive self-adjoint operator on a Hilbert space \(\mathcal H\) and let \(a\) be a positive constant. Let \(f_1\) and \(f_2\) be arbitrary and let \(u=u(t)\) be the unique solution of the initial value problem \[ (D^{\gamma})^2u+2aD^{\gamma}u+Au=0, \quad u(0)=f_1,\quad D^{\gamma}u(0)=f_2, \quad0<\gamma<1. \] Then there exists \(v=v(t)\), a solution of \(2aD^{\gamma}v+Av=0\), which has the same asymptotic behavior as \(u\), in the sense that \(u(t)=v(t)+o(v(t))\) as \(t\to+\infty\). Here the convergence is in a weak sense.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1866737
zbMATH Keywords: fractional telegraph equation
zbMATH Keywords: fractional derivatives
zbMATH Keywords: Laplace transform method
zbMATH Keywords: asymptotics
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866737