Creator:

Tatar, Nasser-eddine

Contributor:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Title:

Mittag-Leffler stability for a Timoshenko problem

Group publication title:

AMCS, volume 31 (2021)

Subject and Keywords:

Caputo fractional derivative ; Mittag-Leffler stability ; multiplier technique ; resolvent operator

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.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Date:

2021

Resource Type:

artykuł

DOI:

10.34768/amcs-2021-0015

Pages:

219-232

Source:

AMCS, volume 31, number 2 (2021) ; click here to follow the link

Language:

eng

License CC BY 4.0:

click here to follow the link

Rights:

Biblioteka Uniwersytetu Zielonogórskiego