  The classical binomial process has been studied by \citet{jakeman} (and the
references therein) and has been used to characterize a series of radiation
states in quantum optics. In particular, he studied a classical birth-death
process where the chance of birth is proportional to the difference between a
larger fixed number and the number of individuals present. It is shown that at
large times, an equilibrium is reached which follows a binomial process. In
this paper, the classical binomial process is generalized using the techniques
of fractional calculus and is called the fractional binomial process. The
fractional binomial process is shown to preserve the binomial limit at large
times while expanding the class of models that include non-binomial
fluctuations (non-Markovian) at regular and small times. As a direct
consequence, the generality of the fractional binomial model makes the proposed
model more desirable than its classical counterpart in describing real physical
processes. More statistical properties are also derived.
