Square-Mean Asymptotically Almost Periodic Solutions for a Class of Fractional Stochastic Differential Equation

Abstract

The study of the properties for fractional stochastic differential equation is one of the hot directions in the field of mathematics over the years. For a class of linear fractional stochastic differential equation on Hilbert space ，the existence and uniqueness of its square-mean asymptotically almost periodic mild solutions are studied，and then the conclusions of this kind of linear fractional stochastic differential equation are extended to corresponding semi-linear fractional stochastic differential equation. The existence and uniqueness of square-mean asymptotically almost periodic mild solutions for this kind of semi-linear fractional stochastic differential equation are discussed by Banach fixed point theorem，and then discuss the existence of square-mean asymptotically almost periodic mild solutions by using Schauder fixed point theorem under non-Lipschitz conditions.

Keywords

• fractional stochastic differential equation
• square-mean asymptotically almost periodic solutions
• banach fixed point theorem
• schauder fixed point theorem