Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Defterli, OzlemSubject: search.filters.subject.Fractional Hamiltonian

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  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    A Numerical Scheme for Two-Dimensional Optimal Control Problems With Memory Effect
    (Pergamon-elsevier Science Ltd, 2010) Defterli, Ozlem
    A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 111
    Citation - Scopus: 138
    Fractional Optimal Control Problems With Several State and Control Variables
    (Sage Publications Ltd, 2010) Baleanu, Dumitru; Agrawal, Om P.; Defterli, Ozlem
    In many applications, fractional derivatives provide better descriptions of the behavior of dynamic systems than other techniques. For this reason, fractional calculus has been used to analyze systems having noninteger order dynamics and to solve fractional optimal control problems. In this study, we describe a formulation for fractional optimal control problems defined in multi-dimensions. We consider the case where the dimensions of the state and control variables are different from each other. Riemann-Liouville fractional derivatives are used to formulate the problem. The fractional differential equations involving the state and control variables are solved using Grunwald-Letnikov approximation. The performance of the formulation is shown using an example.