  The fractional birth and the fractional death processes are more desirable in
practice than their classical counterparts as they naturally provide greater
flexibility in modeling growing and decreasing systems. In this paper, we
propose formal parameter estimation procedures for the fractional Yule, the
fractional linear death, and the fractional sublinear death processes. The
methods use all available data possible, are computationally simple and
asymptotically unbiased. The procedures exploited the natural structure of the
random inter-birth and inter-death times that are known to be independent but
are not identically distributed. We also showed how these methods can be
applied to certain models with more general birth and death rates. The
computational tests showed favorable results for our proposed methods even with
relatively small sample sizes. The proposed methods are also illustrated using
the branching times of the plethodontid salamanders data of \cite{hal79}.
