Stability Of Timoshenko System With Fractional Derivative Damping

In recent years,fractional derivative operators play an important role in modeling and controlling many physical and biological phenomena.One of the most studied branches of the Fractional calculus is the theory of fractional evolution equations,in which the fractional derivative is used instead of the integral derivative relative to time,the theory has been widely developed in the past forty years.In this thesis,we study the stability of Timoshenko systems with fractional derivative damping.We study the stability results of the system using semigroup methods,multiplier methods,and frequency domain methods and so on.This thesis is divided into four chapters.In chapter 1,the background of fractional derivative is introduced,and the related research is also given.In chapter 2,the stability of thermoelastic Timoshenko system with fractional derivative boundary is studied.The existence of the solution is proved by the semigroup method,and the non-exponential stability and polynomial stability of the system is proved by the frequency domain method and the multiplier method.In Chapter 3,we study the stability of Timoshenko systems with locally singular fractional Kelvin-Voigt damping The existence of solutions is proved using the semigroup method,and the polynomial stability of the system is proved using the multiplier method.In Chapter 4,we give the conclusion and future research question.