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Asymptotic Behaviour of the Time-Fractional Telegraph Equation

Part of: Qualitative behavior Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Vicente Vergara
Vicente Vergara*
Affiliation:
Universidad de Tarapacá
*
∗ Postal address: Universidad de Tarapacá, Instituto de Alta Investigación, Antofagasta N. 1520, Arica, Chile. Email address: vvergaraa@uta.cl
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Abstract

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We obtain the long-time behaviour to the variance of the distribution process associated with the solution of the telegraph equation. To this end, we use a version of the Karamata-Feller Tauberian theorem.

Keywords

Telegraph equationfractional derivativeMittag-Leffler functionTauberian theorem

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 45K05: Integro-partial differential equations 45M05: Asymptotics
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 890 - 893
Copyright
© Applied Probability Trust 

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