On weighted pseudo almost automorphic mild solutions for some mean field stochastic evolution equations

TL;DR

This paper establishes the existence and uniqueness of weighted pseudo almost automorphic mild solutions in distribution for certain mean field stochastic evolution equations driven by fractional Brownian motion, under hyperbolic and Acquistapace-Terreni conditions.

Contribution

It introduces new results on solutions for mean field stochastic equations with fractional Brownian motion, extending the theory to weighted pseudo almost automorphic solutions.

Findings

Existence of solutions under specified conditions

Uniqueness of solutions in distribution

Illustrative examples provided

Abstract

When the evolution familiy is hyperbolic and satisfies the Acquistapace-Terreni conditions, the existence and uniquenness of an almost automorphic mild solution and a weighted pseudo almost automorphic mild solution in distribution of mean-filed nonautonomous stochastic evolution equations driven by fractional Brownian motion is proved. Examples illustrating the main results are included.