Existence in \(\alpha \) -Norm of \(\mu -\) Pseudo Almost Automorphic Mild Solutions for Mean Field Stochastic Evolution Equations

In this work, we use the concept of \(\mu \) -square-mean pseudo almost automorphic processes introduced by Diop et al. (Bull Malaysian Math Sci Soc 41:287–310, 2018) to discuss the existence and uniqueness in \(\alpha \) -norm of mild solutions to mean field stochastic evolution equations. We assume that the linear part generates an analytic semigroup and the nonlinear part is given by Lipschitz continuous functions with respect to the fractional power norm of the linear part. Our results mainly rely upon fractional powers of operators, Wasserstein distance and stochastic analysis. An example is provided to support our findings.