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

Abstract

In this paper, we analyze the classes of (R, B)-multi-almost automorphic functions and asymptotically (R, B)-multi-almost automorphic functions. We provide plenty valuable applications to the abstract Volterra integrodifferential equations in Banach spaces and partial differential equations.