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

A method is presented to give the solution of the initial-value problem of a fractional differential equation, when the initial values are given as values of the function and its integer-order derivatives. It is shown that some of the initial values are required to be put equal to zero in order to obtain a solution. The presentation starts with the ordinary differential equation, and proceeds to the fractional differential equation. Discussions here are restricted to linear equations with constant coefficients, which can be solved with the aid of the Laplace transform.