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The aim of this work is to investigate the existence and uniqueness of  μ -pseudo almost periodic (resp.  μ -pseudo compact almost automorphic) weak solutions for the following partial functional differential inclusion:whereis a strongly maximal monotone operator on a real Hilbert space,is a Stepanov  μ -pseudo almost periodic (resp.  μ -pseudo compact almost automorphic) function of class  r ,is the Banach space of all continuous functions fromtoand the history functionis defined byfor. Two examples are given for parabolic and subdifferential systems.

μ -Pseudo compact almost automorphic weak solutions for some partial functional differential inclusions