The Research Of Controllability Of Two Classes Of Fractional Stochastic Differential Evolution Equations

In this paper,the controllability of the two classes of fractional stochastic evolution equations are investigated.The first equations are fractional hybrid stochastic functional evolution equations,the other equations are fractional impulsive neutral stochastic evolution equations.In most existing literature,the authors used a variety of fixed point theorem to study the approximate controllability of the two types of equations,and assumed that the semigroup generated by the linear part is compact.If we want to consider the controllability of the two types of equations,the range of the inverse operator generated by the control function is not full.The we give the pseudo inverse operator ?-1 that takes values in L2(J,U)/ker? Assuming that the semigroup is not compact,we must adopt the new tool of noncompact to study the controllability of the two types of equations.Therefore,in this paper,we use the measure of noncompact and Monch fixed point theorem to study them.Three parts is introduced in this paper.In the first chapter,The models and properties of the fractional evolution equation,fractional stochastic evolution equations,fractional impulsive evolution equation are introduced.Then,the research progress and the existing problems of the controllability of the fractional hybrid stochastic functional evolution equations and fractional impulsive neutral stochastic evolution equations are given.In the last,the properties of the measure of noncompact and Monch fixed point theorem are listed.In the second chapter,the controllability of fractional hybrid stochastic functional evolution equations is mainly discussed.The expression and related property of the mild solution of the equation are given.The conditions of the drift,the diffusion,pseudo inverse operator ?-1 by control function are listed.According to these conditions,we convert the controllability of the equations to the existence of fixed point.The proof is divided four steps:the operator G maps the closed ball to itself;the operator G is continuous;the operator G is equicontinuous;the operator G satisfies the conditions of Monch fixed point theorem.Finally an example is given to illustrate the effectiveness of the theory.In the third chapter,the controllability of fractional impulsive neutral stochastic evolution equations is mainly discussed.The expression and related property of the mild solution of the equation are given.The conditions of the drift,the diffusion,neutral term,impulsive functions,pseudo inverse operator ?-1 by control function are listed.According to these conditions,we convert the controllability of the equations to the existence of fixed point.The proof is divided four steps:the operator G1 maps the closed ball to itself;the operator G1 is continuous;the operator G1 is equicontinuous on the impulsive interval;the operator G1 satisfies the conditions of Monch fixed point theorem.Finally an example is given to illustrate the effectiveness of the theory.