Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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COAR Access Rights: search.filters.coarAccessRights.open accessSubject: search.filters.subject.Euler-Lagrange Equation

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  • Article
    Citation - WoS: 86
    Citation - Scopus: 97
    On Fractional Derivatives With Generalized Mittag-Leffler Kernels
    (Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, Dumitru
    Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    On the Motion of a Heavy Bead Sliding on a Rotating Wire - Fractional Treatment
    (Elsevier, 2018) Asad, Jihad H.; Alipour, Mohsen; Baleanu, Dumitru
    In this work, we consider the motion of a heavy particle sliding on a rotating wire. The first step carried for this model is writing the classical and fractional Lagrangian. Secondly, the fractional Hamilton's equations (FHEs) of motion of the system is derived. The fractional equations are formulated in the sense of Caputo. Thirdly, numerical simulations of the FHEs within the fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Finally, simulation results verify that, taking into account the fractional calculus provides more flexible models demonstrating new aspects of the real world phenomena.
  • Article
    On fractional derivatives with generalized Mittag-Leffler kernels
    (Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, Dumitru
    Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.