Stepanov-like doubly weighted pseudo almost automorphic mild solutions for fractional stochastic neutral functional differential equations

Abstract

Abstract This paper first investigates the equivalence of the space and translation invariance of Stepanov-like doubly weighted pseudo almost automorphic stochastic processes for nonequivalent weight functions; secondly, based on semigroup theory, fractional calculations, and the Krasnoselskii fixed-point theorem, we obtain the existence and uniqueness of Stepanov-like doubly weighted pseudo almost automorphic mild solutions for a class of nonlinear fractional stochastic neutral functional differential equations under non-Lipschitz conditions. These results enrich the complex dynamics of Stepanov-like doubly weighted pseudo almost automorphic stochastic processes.

Keywords

• Stepanov-like doubly weighted pseudo almost automorphic stochastic process
• Translation invariance
• Existence
• Uniqueness