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

TL;DR

This paper introduces and analyzes classes of $({\mathrm R},{\mathcal B})$-multi-almost automorphic functions, exploring their properties and applications to integral and partial differential equations in Banach spaces.

Contribution

It defines new classes of automorphic functions and demonstrates their usefulness in solving Volterra integrodifferential and partial differential equations.

Findings

Characterization of $({\mathrm R},{\mathcal B})$-multi-almost automorphic functions

Applications to abstract Volterra integrodifferential equations

Applications to partial differential equations

Abstract

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