Study of composite fractional relaxation differential equation using fractional operators with and without singular kernels and special functions

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