WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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2008 - 200912010 - 20181

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Publisher: search.filters.publisher.Sage Publications LtdSubject: search.filters.subject.Fractional Derivatives

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  • Article
    Citation - WoS: 11
    Citation - Scopus: 11
    Steady Periodic Response for a Vibration System With Distributed Order Derivatives To Periodic Excitation
    (Sage Publications Ltd, 2018) Baleanu, Dumitru; Duan, Jun-Sheng
    Steady-state periodic responses for a vibration system with distributed order derivatives are investigated, where the fractional derivative operator -infinity D-t(beta) is utilized. The response to complex harmonic excitation is derived and the amplitude-frequency and phase-frequency relations are obtained. For a periodic excitation, we decompose it into the Fourier series, and then make use of the principle of superposition and the results of harmonic excitations to obtain the response. Finally, we examine three numerical examples by using the proposed method.
  • Conference Object
    Citation - WoS: 7
    Citation - Scopus: 7
    Nonconservative Systems Within Fractional Generalized Derivatives
    (Sage Publications Ltd, 2008) Baleanu, Dumitru; Muslih, Sami I.
    A fractional derivative generalizes an ordinary derivative, and therefore the derivative of the product of two functions differs from that for the classical ( integer) case ; the integration by parts for Riemann-Liouville fractional derivatives involves both the left and right fractional derivatives. Despite these restrictions, fractional calculus models are good candidates for description of nonconservative systems. In this article, nonconservative Lagrangian mechanics are investigated within the fractional generalized derivative approach. The fractional Euler-Lagrange equations based on the Riemann-Liouville fractional derivatives are briefly presented. Using generalized fractional derivatives, we give a meaning for the term which appears in fractional Euler-Lagrange equations and contains the second order fractional derivative. The fractional Lagrangians and Hamiltonians of two illustrative nonconservative mechanical systems are investigated in detail.