A comparative study of the fractional oscillators

Abstract

In this work, we have investigated the fractional differential equation to describe the motion of a linear oscillator using fractional derivative operators with or without singular kernels. In order to be consistent with the physical systems the value of the fractional parameter that characterizes the existence of fractional structures in the system, lies within unit interval. The solutions of the non-integer order differential equation are obtained and expressed in terms of generalized G function depending upon the fractional parameter. The classical cases could be recovered by making the limit of fractional parameter approaches to unity. Moreover, we will analyse and compare the behaviour of the oscillator with different definitions of the fractional operators via graphical illustrations, phase portraits and Poincare maps.

Keywords

• Linear oscillator
• Fractional derivative
• Power law kernel
• Non-singular kernel
• Phase portraits