Influence of fractional order parameter on the dynamics of different vibrating systems

Abstract

In this work, we will investigate the fractional differential equations associated to different vibration phenomena. More specifically, we will discuss Bagley-Torvik equation, composite fractional relaxation differential equation and the motion of a linear oscillator using fractional derivative operator in the sense of Atangana-Baleanu. 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 functions depending upon the fractional parameter. The classical cases could be recovered by making the limit of fractional parameter approaches to unity. Moreover, we will analyze and compare the control of the fractional order parameter on the dynamics of the models and useful conclusions are recorded.