Department of Modeling and Design Engineering Systems
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Browsing Department of Modeling and Design Engineering Systems by Author "AGİLA, Adel"
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Item FRACTIONAL MODELING OF OSCILLATING DYNAMIC SYSTEMS(2015-06-25) AGİLA, Adel; İRFANOĞLU, Bülent; EİD, RajehIn recent years, a special attention is given to model fractional dynamical systems. These systems include fractional oscillating dynamical systems. Many methods are used to model the fractional oscillating dynamical systems. The responses of some systems are obtained by means of fractional calculus and calculus of variations. In this thesis, fractional representations based on fractional calculus, calculus of variations are classified into two types: The first type is the fractional Euler-Lagrange equations representations of free oscil lating fractional systems. The fractional representation appears in the coefficients of damping terms of variable coefficient second order homogeneous differential equa tions. In the second type, the differential operators are subjected to fractional orders. The considered case studies are models given by second order homogeneous and non homogeneous three-term fractional order differential equations with fractional damp ing terms. The two types are combined to produce extended fractional Euler-Lagrange equations models. In these models the differential operators are subjected to fractional orders in the damping term of the system. Additionally, the time varying coefficients of the damping terms contain a fractional integral order. A hybrid method is introduced to obtain the responses of fractional oscillating sys tems. These systems are modeled by means of second order homogeneous three-term fractional order differential equations with fractional damping terms. The responses are compared with Wright function based solutions.