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In this paper, we analyze the classes of $({\mathrm R},{\mathcalB})$-multi-almost automorphic functions and asymptotically $({\mathrmR},{\mathcal B})$-multi-almost automorphic functions. We provide plentyvaluable applications to the abstract Volterra integrodifferential equations inBanach spaces and partial differential equations.

$({\mathrm R},{\mathcal B})$-Multidimensional-almost automorphic functions with applications to integral and partial differential equations