Dynamical Behavior Of Two Classes Of Fractional Differential Equations

In this paper, we firstly introduce the fractional derivative, and then we study the stochastic fractional Ginzburg-Landau equation and the stochastic coupled fractional Ginzburg-Landau equation with fractional derivative. We first transform the stochastic coupled fractional Ginzburg-Laudau equation into random equation which solutions generate a random parameter. Then we prove the existence of the random attractor for the random dynamical system.This paper is organized as follows:In the first chapter, we introduce the fractional derivative and the format, the physical context of the Ginzburg-Landau equation, and the random dynamic system.In the second chapter, we first introduce the fractional derivatuve, the works and the existence of local solutions. Then we use the Holder ineuquality to estimate the solution of the equation and get the estimate upper bound of the blow-up solution.In the third chapter,we transform the stochastic fractional Ginzburg-Landau equation with additive noise into random equation which solutions generate a random dynamical system, then we obtain the existence of the random attractor for the random dynamical system.In the fourth chapter, we study the stochastic coupled fractional Ginzburg-Landau equation with additive noise, then we obtain the existence of the random attractor for the random dynamical system.In the fifth chapter, we conclude our works in this paper and give some further plan on our next research.