  This paper presents a new type of Gronwall-Bellman inequality, which arises
from a class of integral equations with a mixture of nonsingular and singular
integrals. The new idea is to use a binomial function to combine the known
Gronwall-Bellman inequalities for integral equations having nonsingular
integrals with those having singular integrals. Based on this new type of
Gronwall-Bellman inequality, we investigate the existence and uniqueness of the
solution to a fractional stochastic differential equation (SDE) with fractional
order on (0, 1). This result generalizes the existence and uniqueness theorem
related to fractional order (1/2 1) appearing in [1]. Finally, the fractional
type Fokker-Planck-Kolmogorov equation associated to the solution of the
fractional SDE is derived using It^o's formula.
