  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.
