  In the current research work, our basic objective is to investigate the
stucture of Hom-associative trialgebras. Next, we build up one important class
of Hom-associative trialgebras and provide properties of right, left and meddle
operations in Hom-associative trialgebras. Furthermore, we describe the
classification of $n$-dimensional Hom-associative trialgebras for $n\leq 3$.
Additionally, the properties of the Inner-derivations and centroids are
identified and discussed. Eventually the Inner-derivations and centroids are
computed.
