Fractional Laplace transform method in the framework of the CTIT transformation

We propose an adapted Laplace transform method that gives the solution of a linear fractional differential equation with constant coefficients in terms of exponential function. After we mention what the utilized transformation, the CTIT transformation, is based on, we explain how it can reduce the problem from fractional form to ordinary form when it is used with Laplace transformation, via some examples for 0 < alpha < 2 where a is the order of fractional derivative. Finally, we illustrate the applications of our results. (C) 2016 Elsevier B.V. All rights reserved.