Mittag-Leffler stability for a Timoshenko problem

International Journal of Applied Mathematics and Computer Science

Tatar Nasser-Eddine¹ 

[1] Department of Mathematics and Statistics, King Fahd University of Petroleum and MineralsDhahran31261, Saudi Arabia;

关键词: caputo fractional derivative;    mittag-leffler stability;    multiplier technique;    resolvent operator;   

DOI  :  10.34768/amcs-2021-0015

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown