Existence,Uniqueness And Stability Of Solutions For Stochastic Fractional Order Nonlinear Systems

In recent decades,stochastic models have been widely used in many fields.For example,social sciences,physical sciences,finance,machinery,etc..Under the above social background,first of all,we consider a class of stochastic fractional nonlinear systems driven by second-order moment processes,under the condition that the coefficients satisfy Lipschitz condition and linear growth condition,by using successive approximation method and iterative method,combining BorelCantelli lemma and some classical inequalities,the existence and uniqueness theorems of solutions for two classes of stochastic fractional-order nonlinear systems driven by second-order moment processes are given.However,because the global Lipschitz condition has great limitations in practical application,the existence and uniqueness theorems of solutions for stochastic fractional order nonlinear systems are given again under the condition that the coefficients satisfy the local Lipschitz condition and the linear growth condition.Secondly,in view of the importance of stability analysis in the study of stochastic models,two classes of stability criteria for solutions under local Lipschitz condition are given.