Polynomial stability of thermoelastic Timoshenko system with fractional derivative boundary control

Abstract

In this paper, we consider a thermoelastic Timoshenko system with control boundary conditions of fractional derivative type. By introducing two new equations to deal with the control boundary conditions of fractional derivative type, we obtain a new system equivalent to the original thermoelastic Timoshenko system. The well-posedness of solution of system follows from the semigroup method. The polynomial stability result of system are given by frequency domain method and multiplier technique, while the decay rate depending on the order of fractional derivative is optimal than the previous literatures.