1. bookVolume 31 (2021): Issue 2 (June 2021)
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05 Apr 2007
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access type Open Access

Mittag-Leffler stability for a Timoshenko problem

Published Online: 08 Jul 2021
Page range: 219 - 232
Received: 20 Feb 2021
Accepted: 30 Mar 2021
Journal Details
License
Format
Journal
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
Abstract

A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.

Keywords

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