  This paper derives the non-analytic solution to the Fokker-Planck equation of
fractional Brownian motion using the method of Laplace transform. Sequentially,
by considering the fundamental solution of the non-analytic solution, this
paper obtains the transition probability density function of the random
variable that is described by the It\^o's stochastic ordinary differential
equation of fractional Brownian motion. Furthermore, this paper applies the
derived transition probability density function to the Cox-Ingersoll-Ross model
governed by the fractional Brownian motion instead of the usual Brownian
motion.
