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Number 2 - June 2021
Volume 31 - 2021
Mittag-Leffler stability for a Timoshenko problem
Nasser-eddine Tatar
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
Caputo fractional derivative, Mittag-Leffler stability, multiplier technique, resolvent operator