Zafar, Azhar AliAwrejcewicz, Jan2021-12-022021-12-022021Zafar A.A., Awrejcewicz J., Influence of fractional order parameter on the dynamics of different vibrating systems. W: DSTA-2021 Conference Books – Abstracts (16th International Conference : Dynamical Systems Theory and Applications DSTA 2021 ABSTRACTS), Awrejcewicz J. (red.), Kaźmierczak M. (red.), Olejnik P. (red.), Mrozowski J. (red.), Wydawnictwo Politechniki Łódzkiej ; Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki, Łódź 2021, s. 64-65, ISBN 978-83-66741-20-1.978-83-66741-20-1http://hdl.handle.net/11652/4117In 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.enAll rights reservedFair use conditionWszystkie prawa zastrzeżoneDla wszystkich w zakresie dozwolonego użytkufractional derivative operatorvibrating systemslinear oscillatorsoperator różniczkowania ułamkowegoukłady wibracyjneoscylatory linioweAbstraktLUT LicenseLicencja PŁLodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.