Solutions for Cauchy Problems of Composite Fractional Differential Equations

Firstly,we give some definitions and properties for the fractional integral and differential. Secondly,some errors in Refs[1]and[13]are corrected by Laplace transform and Hankel integral formula of T function,and general existence and nonexistence theorems of solutions are given.Finally,we obtain the explicit solution of the initial value problem for variable coefficients fractional differential equations with composite fractional derivative operator by Laplace transform and successive approximation method.