Existence And Stability Of S-asymptotically Periodic Solutions For Two Kinds Of Stochastic Evolution Equations

Fractional calculus has a history of more than 300 years.As a promotion of integer order calculus,it has a strong physical background.Fractional derivatives can more effectively describe the memory and genetic properties of substances and processes,so the application of fractional calculus in physics,chemistry,engineering,biology,finance and other fields has become more extensive.In this paper,two types of stochastic evolution equations driven by fractional Brownian motion are studied,and the relevant properties of the S-asymptotic -periodic solutions of these equations are studied.The first part studies the first-order non-autonomous stochastic evolution equation driven by fractional Brownian motion.It mainly uses the evolution family theory,Gronwall inequality and Banach fixed point theorem to verify the existence,uniqueness and stability of the mean square periodic solution.The second part studies the fractional-order autonomous stochastic evolution equation driven by fractional Brownian motion.First,the p-mean S-asymptotic -periodic solution is expressed by the Mittag-Leffler function,and then the semigroup theory of operators,Gronwall inequality Banach fixed point theorem proves the existence,uniqueness and stability of p-mean S-asymptotic -periodic solutions.