In this paper we introduce and study a new concept called Stepanov-like C (n)-pseudo almost automorphy, which generalizes in a natural fashion both the notions of C (n)-pseudo almost periodicity and that of C (n)-pseudo almost automorphy recently introduced in the literature by the authors. Basic properties of these new functions are investigated. Furthermore, we study and obtain the existence of C (N +m)-pseudo almost automorphic solutions to some nonautonomous higher-order systems of differential equations with Stepanov-like C (m)-pseudo almost automorphic coefficients.

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