Solution for the initial-value problem of a fractional differential equation

In a preceding report, a method was presented to give the solution for the initial-value problem of a fractional differential equation when the initial values were the values of the function and its integer-order derivatives. It is now shown that the solution can be obtained in a less restricted condition. The discussions here are restricted to linear equations with constant coefficients, which can be solved with the aid of the Laplace transform. The main discussions are given when we adopt the Riemann-Liouville fractional derivative, and some comments are added when we use the Caputo derivative or its modification.