Doss almost periodic functions, Besicovitch-Doss almost periodic functions and convolution products

TL;DR

This paper investigates how Doss and Besicovitch-Doss almost periodic functions behave under convolution, especially for operators with specific growth rates, aiding the analysis of fractional differential equations.

Contribution

It extends previous work by analyzing invariance of these functions under convolution for operators with particular growth, applicable to fractional differential equations.

Findings

Invariance of Doss almost periodicity under convolution for certain operators.

Extension of results to fractional differential equations in Banach spaces.

Analysis of functions with specific growth rates at zero and infinity.

Abstract

In the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies \cite{fedorov-novi} and \cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to \cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equations in Banach spaces.