A method for solving differential equations of fractional order

Abstract

In this paper, we consider Caputo type fractional differential equations of order 0<α<1 with initial condition x(0)=x0. We introduce a technique to find the exact solutions of fractional differential equations by using the solutions of integer order differential equations. Generalization of the technique to finite systems is also given. Finally, we give some examples to illustrate the applications of our results.