Find in Library

Abstract Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of the non-integer order derivative operator D t α $D_{t}^{\alpha }$ , more specifically we employ the definitions of Caputo, Caputo–Fabrizio and Atangana–Baleanu of non-integer order derivative operators. We apply the Laplace transform method to solve the problem and express our solutions in terms of Lorenzo and Hartley’s generalised G function. Furthermore, the effects of the parameters involved in the model are graphically highlighted.