<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Mittag-Leffler stability for a Timoshenko problem

King Fahd University of Petroleum and Minerals

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Mittag-Leffler stability for a Timoshenko problem"}

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...

Mittag-Leffler stability for a Timoshenko problem

Published Online: Jul 08, 2021

Page range: 219 - 232

Received: Feb 20, 2021

Accepted: Mar 30, 2021

DOI: https://doi.org/10.34768/amcs-2021-0015

Keywords
Caputo fractional derivative, Mittag-Leffler stability, multiplier technique, resolvent operator

© 2021 Nasser-Eddine Tatar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mittag-Leffler stability for a Timoshenko problem

Published Online: Jul 08, 2021

Page range: 219 - 232

Received: Feb 20, 2021

Accepted: Mar 30, 2021

DOI: https://doi.org/10.34768/amcs-2021-0015

KeywordsCaputo fractional derivative, Mittag-Leffler stability, multiplier technique, resolvent operator

© 2021 Nasser-Eddine Tatar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Caputo fractional derivative, Mittag-Leffler stability, multiplier technique, resolvent operator