WoS İndeksli Yayınlar Koleksiyonu

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

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2010 - 20193

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Publisher: search.filters.publisher.SpringerSubject: search.filters.subject.Fractional Derivatives

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 15
    Citation - Scopus: 17
    Fractional Dynamics of an Erbium-Doped Fiber Laser Model
    (Springer, 2019) Saad, K. M.; Baleanu, D.; Gomez-Aguilar, J. F.
    In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville-Caputo (LC), Caputo-Fabrizio-Caputo (CFC) and Atangana-Baleanu-Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method (HATM) to calculate approximate solutions for the TFDEFL model. This method gives the solution in the form of a rapidly convergent series that can ensure the convergence in solving the resultant series. We study the convergence analysis of HATM by computing the interval of convergence through the h-curves, the residual error function and the average residual error, respectively. We also show the effectiveness and accuracy of this method by comparing the approximate solutions based upon the LC, CFC and ABC time-fractional derivatives.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 31
    Hamilton-Jacobi and Fractional Like Action With Time Scaling
    (Springer, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.; Herzallah, Mohamed A. E.
    This paper represents the Hamilton-Jacobi formulation for fractional variational problem with fractional like action written as an integration over a time scaling parameter. Also we developed the fractional Hamiltonian formulation for the fractional like action. In all the given calculations, the most popular Riemann-Liouville (RL) and Caputo fractional derivatives are employed. An example illustrates our approach.
  • Article
    Citation - WoS: 65
    Citation - Scopus: 72
    Newtonian Law With Memory
    (Springer, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Nigmatullin, Raoul R.; Baleanu, Dumitru
    In this study we analyzed the Newtonian equation with memory. One physical model possessing memory effect is analyzed in detail. The fractional generalization of this model is investigated and the exact solutions within Caputo and Riemann-Liouville fractional derivatives are reported.