  In the paper, we considered the existence and uniqueness of the global
solution in the space of continuously differentiable functions for a nonlinear
differential equation with the Caputo fractional derivative of general form.
Our main method is to derive an integral equation corresponding to the original
nonlinear fractional differential equation and to prove their eqivalence. Once
we prove the equivalence, then the proof of existence and uniquness of solution
can be done by standard way of using Banach fixed point theorem.
