Influence of Fractional Order Parameter on the Dynamics of Different Vibrating Systems

The aim of this work is to investigate the fractional differential equations associated to different vibration phenomena. More specifically, we will discuss Bagley-Torvik equation, composite fractional relaxation oscillator, the motion of a linear oscillator and generalized form of Scott-Blair oscillator and Kelvin-Voigt oscillator using fractional derivative operator in the sense of Atangana-Baleanu. To maintain the consistency of the physical systems the value of the fractional order parameters (that specify the existence of non-integer order structures of the system) lies within unit interval. The solutions of the non-integer order differential equation are obtained by using integral transforms and Gacer-Stefest’s algorithm. Moreover, the classical cases could be recovered by using the interpolation property of non-integer order derivative operator. Furthermore, we will compare and analyze the control of the fractional order parameters on the dynamics of the models under consideration. Finally, useful conclusions and recommendations are recorded.