Browsing by Author "Agila, Adel"

Now showing 1 - 3 of 3

Citation - WoS: 14
Citation - Scopus: 18
A Freely Damped Oscillating Fractional Dynamic System Modeled By Fractional Euler-Lagrange Equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; 56389; Matematik
The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
Citation - WoS: 48
Citation - Scopus: 55
Applications of the Extended Fractional Euler-Lagrange Equations Model to Freely Oscillating Dynamical Systems
(Editura Acad Romane, 2016) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; 56389; Matematik
The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated.
Citation - WoS: 0
Citation - Scopus: 0
Controlled Forced Fractional Vibrating System
(Editura Acad Romane, 2019) Agila, Adel; Baleanu, Dumitru; 56389; Matematik
The reliability of dynamic systems is enhanced by vibration control. Many types of controllers are used to control the dynamic systems' vibrations. The integer and fractional PID controllers are used to control the fractional and integer dynamic systems. Different techniques are utilized to model the controlled systems. In this study, the discrete integer proportional integral derivative (PID) controller is used to control a forced damped variable-order fractional oscillatory systems. The objectives of this study are the analysis of controlled fractional system responses, and the investigation of controller gains' effects on system response characteristics. The Caputo-Fabrizio fractional derivative is used to model the system fractional dissipating force. The system responses are approximated by numerical and time discretization techniques. In order to verify the feasibility and effectiveness of the introduced methods, the fractional system response and integer system response are compared at fractional order close to one. The controlled responses of the fractional system are obtained for different fractional derivative order values. The results demonstrate same effects of PID gains on the fractional and integer oscillatory system responses' metrics. However, the system responses are varying based on the fractional derivative order values. The study shows that the integer response and the fractional responses have same behaviors and different instantaneous values.