  This paper introduces the Generalized Fractional Compound Poisson Process
(GFCPP), which claims to be a unified fractional version of the compound
Poisson process (CPP) that encompasses existing variations as special cases. We
derive its distributional properties, generalized fractional differential
equations, and martingale properties. Some results related to the governing
differential equation about the special cases of jump distributions, including
exponential, Mittag-Leffler, Bernst\'ein, discrete uniform, truncated
geometric, and discrete logarithm. Some of processes in the literature such as
the fractional Poisson process of order $k$, P\'olya-Aeppli process of order
$k$, and fractional negative binomial process becomes the special case of the
GFCPP. Classification based on arrivals by time-changing the compound Poisson
process by the inverse tempered and the inverse of inverse Gaussian
subordinators are studied. Finally, we present the simulation of the sample
paths of the above-mentioned processes.
