Mean-Square Asymptotically Almost Automorphic Solutions to Fractional Stochastic Relaxation Equations

Abstract

Mild solutions generated by a $\left(a, k\right)$-regularized family to fractional stochastic relaxation equations are studied. The main objective is to establish the existence and uniqueness of square-mean asymptotically almost automorphic mild solutions to linear and semilinear case of these equations. Under different hypotheses, some new theorems concerning the main objective are derived.