Baleanu, DumitruSajjadi, Samaneh SadatJajarmi, AminDefterli, Özlem2022-10-062022-10-062021Baleanu, Dumitru...et al. (2021). "On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control", Advances in Difference Equations, Vol. 2021, No. 1.1687-1839http://hdl.handle.net/20.500.12416/5805In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo–Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.eninfo:eu-repo/semantics/openAccessChaotic OscillationExponential KernelFractional CalculusOptimal ControlQuarter-Car Suspension SystemState-Feedback ControlArticle2021110.1186/s13662-021-03393-x