Generalized weighted pseudo-almost periodic solutions and generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions

TL;DR

This paper investigates the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions for abstract Volterra integro-differential inclusions, focusing on their properties and applications in Banach spaces.

Contribution

It introduces new conditions for the existence and uniqueness of these solutions and explores their properties in the context of convolution products.

Findings

Established criteria for solution existence and uniqueness.

Analyzed weighted pseudo-almost automorphic properties of convolution products.

Provided examples demonstrating applications of the theoretical results.

Abstract

In this paper, we analyze the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions in Banach spaces. The main results are devoted to the study of various types of weighted pseudo-almost periodic (automorphic) properties of convolution products. We illustrate our abstract results with some examples and possible applications.