Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions of fractional stochastic evolution equations

Abstract

This paper investigates the abstract fractional stochastic evolution equations. A new existence result of the square-mean S-asymptotically periodic mild solutions are obtained under the assumption that the nonlinear terms only satisfy some growth conditions. Moreover, the uniqueness and asymptotic stability results of the square-mean S-asymptotically periodic solution are presented when the nonlinear functions satisfy the general Lipschitz condition. Finally, two examples are given to illustrate our main results. MR(2020) Subject Classification: 60H15; 47D06; 34G20; 46T20.