Abstract
In this work, we have investigated the fractional differential equation to motion of a linear oscillator using fractional derivative operators with or without singular In order to be consistent with the physical systems the value of the fractional parameter acterizes the existence of fractional structures in the system, lies within unit interval. The of the non-integer order differential equation are obtained and expressed in terms of generalized function depending upon the fractional parameter. The classical cases could be recovered ing the limit of fractional parameter approaches to unity. Moreover, we will analyse and the behaviour of the oscillator with different definitions of the fractional operators via illustrations, phase portraits and Poincare maps. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).