Existence and Uniqueness of the Solution to a Nonlinear Differential   Equation with Caputo Fractional Derivative in the Space of Continuously   Differentiable Functions
  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. 
Sunae Pak and Myongha Kim
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