International Journal of applied mathematics and computer science

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Paper details

Number 2 - June 2021
Volume 31 - 2021

Mittag-Leffler stability for a Timoshenko problem

Nasser-eddine Tatar

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.

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