WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Controlled Forced Fractional Vibrating System(Editura Acad Romane, 2019) Agila, Adel; Baleanu, Dumitru; Baleanu, Dumitru; MatematikThe 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.Article Citation - WoS: 61Citation - Scopus: 83Impulsive Caputo-Fabrizio Fractional Differential Equations in B-Metric Spaces(de Gruyter Poland Sp Z O O, 2021) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Karaplnar, ErdalWe deal with some impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces. We make use of alpha-phi-Geraghty-type contraction. An illustrative example is the subject of the last section.Article Citation - WoS: 66Citation - Scopus: 77Numerical Approach of Fokker-Planck Equation With Caputo-Fabrizio Fractional Derivative Using Ritz Approximation(Elsevier, 2018) Jafari, H.; Lia, A.; Baleanu, D.; Firoozjaee, M. A.In this manuscript, a type of Fokker-Planck equation (FPE) with Caputo-Fabrizio fractional derivative is considered. We present a numerical approach which is based on the Ritz method with known basis functions to transform this equation into an optimization problem. It leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by solving the algebraic system. The convergence of this technique is discussed extensively. Three examples are included to show the applicability and validity of this method. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 48Citation - Scopus: 57Solving Fdes With Caputo-Fabrizio Derivative by Operational Matrix Based on Genocchi Polynomials(Wiley, 2018) Roshan, Sedighe Sadeghi; Jafari, Hossein; Baleanu, Dumitru; Sadeghi Roshan, SedigheWe introduce a new approach to solve a type of fractional order differential equations without singularity. For fractional integration, we obtain the operational matrix through Genocchi polynomials. Some examples are presented to test the applicability and efficiency of the technique.Article Citation - WoS: 268Citation - Scopus: 281Caputo-Fabrizio Derivative Applied To Groundwater Flow Within Confined Aquifer(Asce-amer Soc Civil Engineers, 2017) Baleanu, Dumitru; Atangana, AbdonThe model of the movement of subsurface water via the geological formation called aquifer was extended using a newly proposed derivative with fractional order. An alternative derivative to that of Caputo-Fabrizio with fractional order was presented. The relationship between both derivatives was presented. The new equation was solved analytically using some integral transforms. The exact solution is therefore compared to experimental data obtained from the settlement of the University of the Free State in South Africa. The numerical simulation shows the agreement of the experimental data with an analytical solution for some values of fractional order. (C) 2016 American Society of Civil Engineers.